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nature of mathematics

Questions and Answers of Nature Of Mathematics

Use the right triangle in Figure 7.57 to answer the questions in Problems 6-16.Figure 7.57What is the side opposite ∠B∠B ? A b a B
Use the right triangle in Figure 7. 57 to answer the questions in Problems 6-16.Figure 7.57What is the side adjacent to ∠A∠A ? A b a B
Use the right triangle in Figure 7.57 to answer the questions in Problems 6-16.Figure 7.57What is the side adjacent to ∠B∠B ? A b a B
Use the right triangle in Figure 7.57 to answer the questions in Problems 6-16.Figure 7.57What is the hypotenuse? A b a B
Use the right triangle in Figure 7. 57 to answer the questions in Problems 6-16.Figure 7.57What is sinAsin⁡A ? A b a B
Use the right triangle in Figure 7.57 to answer the questions in Problems 6-16.Figure 7.57What is sinBsin⁡B ? A b a B
Use the right triangle in Figure 7.57 to answer the questions in Problems 6-16.Figure 7.57What is cosAcos⁡A ? A b a B
Use the right triangle in Figure 7.57 to answer the questions in Problems 6-16.Figure 7.57What is cosBcos⁡B ? A b a B
Use the right triangle in Figure 7.57 to answer the questions in Problems 6-16.Figure 7.57What is tanAtan⁡A ? A b a B
Use the right triangle in Figure 7.57 to answer the questions in Problems 6-16.Figure 7.57What is tanBtan⁡B ? A b a B
Find the trigonometric ratios in Problems 17-28 by using a calculator. Round your answers to four decimal places.sin56∘sin⁡56∘
Find the trigonometric ratios in Problems 17-28 by using a calculator. Round your answers to four decimal places.sin15∘sin⁡15∘
Find the trigonometric ratios in Problems 17-28 by using a calculator. Round your answers to four decimal places.sin61∘sin⁡61∘
Find the trigonometric ratios in Problems 17-28 by using a calculator. Round your answers to four decimal places.sin18∘sin⁡18∘
Find the trigonometric ratios in Problems 17-28 by using a calculator. Round your answers to four decimal places.cos54∘cos⁡54∘
Find the trigonometric ratios in Problems 17-28 by using a calculator. Round your answers to four decimal places.cos8∘cos⁡8∘
Find the trigonometric ratios in Problems 17-28 by using a calculator. Round your answers to four decimal places.cos90∘cos⁡90∘
Find the trigonometric ratios in Problems 17-28 by using a calculator. Round your answers to four decimal places.cos34∘cos⁡34∘
Find the trigonometric ratios in Problems 17-28 by using a calculator. Round your answers to four decimal places.tan24∘tan⁡24∘
Find the trigonometric ratios in Problems 17-28 by using a calculator. Round your answers to four decimal places.tan52∘tan⁡52∘
Find the trigonometric ratios in Problems 17-28 by using a calculator. Round your answers to four decimal places.tan75∘tan⁡75∘
Find the trigonometric ratios in Problems 17-28 by using a calculator. Round your answers to four decimal places.tan89∘tan⁡89∘
Find the angles (to the nearest degree) for the information given in Problems 29-37.sin−112sin−1⁡12
Find the angles (to the nearest degree) for the information given in Problems 29-37.cos−11cos−1⁡1
Find the angles (to the nearest degree) for the information given in Problems 29-37.tan−11tan−1⁡1
Find the angles (to the nearest degree) for the information given in Problems 29-37.cos−1√22cos−1⁡22
Find the angles (to the nearest degree) for the information given in Problems 29-37.tan−1tan−1
Find the angles (to the nearest degree) for the information given in Problems 29-37.sin−1sin−1
Find the angles (to the nearest degree) for the information given in Problems 29-37.tan−1tan−1
Find the angles (to the nearest degree) for the information given in Problems 29-37.sin−10.35sin−1⁡0.35
Find the angles (to the nearest degree) for the information given in Problems 29-37.cos−10.8cos−1⁡0.8
In Problems 38–47, decide if the given triangle is a right triangle. If it is, find the sine, cosine, and tangent for the angle A. A 13 12 B 5 C
In Problems 38–47, decide if the given triangle is a right triangle. If it is, find the sine, cosine, and tangent for the angle A. B 13 12 A 5 C
In Problems 38–47, decide if the given triangle is a right triangle. If it is, find the sine, cosine, and tangent for the angle A. A 5 4 B 3 C
In Problems 38–47, decide if the given triangle is a right triangle. If it is, find the sine, cosine, and tangent for the angle A. 2 5 6 B
In Problems 38–47, decide if the given triangle is a right triangle. If it is, find the sine, cosine, and tangent for the angle A. B 1 2 V3 A
In Problems 38–47, decide if the given triangle is a right triangle. If it is, find the sine, cosine, and tangent for the angle A. 35 6 C 1 B
In Problems 38–47, decide if the given triangle is a right triangle. If it is, find the sine, cosine, and tangent for the angle A. 1 C 2 3 B
In Problems 38–47, decide if the given triangle is a right triangle. If it is, find the sine, cosine, and tangent for the angle A. 1 C 2 V3 A
In Problems 38–47, decide if the given triangle is a right triangle. If it is, find the sine, cosine, and tangent for the angle A. 1 A C 6 N37 B
In Problems 38–47, decide if the given triangle is a right triangle. If it is, find the sine, cosine, and tangent for the angle A. B 12 C 9 17 A
If the angle from the horizontal to the top of a building is 38° and the horizontal distance from its base is 90 ft, what is the height of the building (to the nearest foot)?
If the angle from the horizontal to the top of a tower is 52° and the horizontal distance from its base is 85 ft, what is the height of the tower (to the nearest foot)?
From a cliff 150 m above the shoreline, a ship’s angle ofdepression is 37°. Find the distance of the ship (to the nearestmeter) from a point directly below the observer.
From a police helicopter flying at 1,000 ft, a stolen car is sighted atan angle of depression of 71°. Find the distance of the car (to thenearest foot) from a point directly below the helicopter.
A 16-ft ladder on level ground is leaning against a house. If theladder’s angle of elevation is 52°, how far above the ground (tothe nearest inch) is the top of the ladder?
Find the height of the Space Needle (to the nearest foot) ifits angle of elevation at 1,000 ft from a point on the grounddirectly below the top is 31. 17°.
The world’s tallest chimney is in Kazakhstan. Find its height (tothe nearest foot) if its angle of elevation at 1,000 ft from a pointon the ground directly below the top stack is 54.01°.
The angle of elevation of the top of the Great Pyramid of Khufu (or Cheops) from a point on the ground 351 ft from a point directly below the top is 52.0°. Find the height of the pyramid (to the
In a 30°-60°-90° triangle, the length of the side adjacent to the 30° angle is √3 times the length of the side opposite the 30° angle. Use this information to find the exact values for cos
What is the radius of the largest circle you can cut from a rectangular poster board with measurements 11 in. by 17 in.? (See Figure 7.58.)Figure 7.58 O
What is the width of the largest rectangle with length 16 in. you can cut from a circular piece of cardboard having a radius of 10 in.? (See Figure 7.59.) Figure 7.59
a. If the distance from the earth to the sun is 92.9 million miles, and the angle formed between Venus, the earth, and the sun is 47° (as shown in Figure 7.60), find the distance from the sun to
Is the woman in the figure a young woman or an old woman?Why do you think this problem is included in the problem set? How does this question relate to working problems in geometry?
Is the fly in Figure 7.11 on the cube or in the cube?Figure 7.11Why do you think this problem is included in the problem set? How does this question relate to working problems in geometry?
Describe what you see in the following illustration. wita
Describe what you see in the following illustration.
Describe a procedure for constructing a line segment congruent to a given segment.
Describe a procedure for constructing a circle with a radius congruent to a given segment.
Discuss what it means to be an undefined term. What is the difference between an axiom and a theorem?
What are the two categories into which geometry is usually separated?
In Problems 9–10, label each cartoon as illustrating a translation, reflection, rotation, dilation, or contraction. 3+8=11 3+8=11
In Problems 9–10, label each cartoon as illustrating a translation, reflection, rotation, dilation, or contraction. NNNNN nh. NNNNN NNNNN
Use the illustration in Figure 7.12 to draw the figures requested in Problems 11–19.Figure 7.12 PQ
Use the illustration in Figure 7.12 to draw the figures requested in Problems 11–19.Figure 7.12 RS
Use the illustration in Figure 7.12 to draw the figures requested in Problems 11–19.Figure 7.12 PQ
Use the illustration in Figure 7.12 to draw the figures requested in Problems 11–19.Figure 7.12 RS
Use the illustration in Figure 7.12 to draw the figures requested in Problems 11–19.Figure 7.12 PQ
Use the illustration in Figure 7.12 to draw the figures requested in Problems 11–19.Figure 7.12 SR
Use the illustration in Figure 7.12 to draw the figures requested in Problems 11–19.Figure 7.12
Use the illustration in Figure 7.12 to draw the figures requested in Problems 11–19.Figure 7.12 PS
Find at least one line of symmetry for each of the illustrations in Problems 20–27, if possible. If there is no line of symmetry,so state.
Find at least one line of symmetry for each of the illustrations in Problems 20–27, if possible. If there is no line of symmetry,so state.
Find at least one line of symmetry for each of the illustrations in Problems 20–27, if possible. If there is no line of symmetry,so state.
Find at least one line of symmetry for each of the illustrations in Problems 20–27, if possible. If there is no line of symmetry,so state.
Find at least one line of symmetry for each of the illustrations in Problems 20–27, if possible. If there is no line of symmetry,so state.
Find at least one line of symmetry for each of the illustrations in Problems 20–27, if possible. If there is no line of symmetry,so state.
Find at least one line of symmetry for each of the illustrations in Problems 20–27, if possible. If there is no line of symmetry,so state.
Find at least one line of symmetry for each of the illustrations in Problems 20–27, if possible. If there is no line of symmetry,so state. + J
Carry out the constructions requested in Problems 28–39. A line segment congruent to AB A B
Carry out the constructions requested in Problems 28–39. A line segment congruent to CD C D
Carry out the constructions requested in Problems 28–39. A line segment congruent to EF E F
Carry out the constructions requested in Problems 28–39. A line segment congruent to GH G H
Carry out the constructions requested in Problems 28–39. Circle with radius congruent to WX W X
Carry out the constructions requested in Problems 28–39. Circle with radius congruent to UV U V
Carry out the constructions requested in Problems 28–39. Circle with radius congruent to ST S T
Carry out the constructions requested in Problems 28–39. Circle with radius congruent to YZ Y N
Carry out the constructions requested in Problems 28–39. Line through P parallel to l P
Carry out the constructions requested in Problems 28–39. Line through Q parallel to m m Q
Carry out the constructions requested in Problems 28–39. Line through R parallel to n R n
Carry out the constructions requested in Problems 28–39. Line through S parallel to k S k
Which of the pictures in Problems 40–47 illustrate a line symmetry? Chambered nautilus
Which of the pictures in Problems 40–47 illustrate a line symmetry?Butterfly 19
Which of the pictures in Problems 40–47 illustrate a line symmetry? Human brain A
Which of the pictures in Problems 40–47 illustrate a line symmetry?Human face
Which of the pictures in Problems 40–47 illustrate a line symmetry?Sculpture by Walter Crane S 16
Which of the pictures in Problems 40–47 illustrate a line symmetry?Sculpture by Indian School EN
Which of the pictures in Problems 40–47 illustrate a line symmetry?Human circulatory system
Which of the pictures in Problems 40–47 illustrate a line symmetry?Empire State Building
Study the patterns shown in Figure 7.13. When folded, they will form cubes spelling CUBE. Letter each pattern in Problems 48–53.Figure 7.13 CUBE CUB 3

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