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mathematics
contemporary mathematics

Questions and Answers of Contemporary Mathematics

Find the missing side and angles in the figure shown. y 6 8.3 a X B: x
Suppose that the plane takes off at a \(23^{\circ}\) angle, and 1 mile from the airport is a 1,500 -foot peak. At what altitude will the plane pass over the peak?
You know the lengths of two sides and the right angle as shown in the figure. Find the length of the third side and the other angles. 4 7
You travel to Chicago and visit the observation deck at Willis Tower, \(1,450 \mathrm{ft}\) above ground. You can see the Magnificent Mile to the northeast \(6,864 \mathrm{ft}\) away. What is the
You are flying a kite on a 60 -foot string. The angle of elevation from the ground to the kite is \(50^{\circ}\). How high above the ground is the kite? 60 ft 50
Identify the type of line containing point \(D\) and point \(A\).Use the graph for the following exercise y 7 6 5 A 4 3 2 D 1 X -7-6-5-4-3-2-1 0 1 2 3 4 4 5 6 7 -1 2 C -3 4 5 -6 -7 E B F
Identify the type of line containing points \(C\) and \(B\).Use the graph for the following exercise. y 7 6 5 A 4 3 2 D 1 X -7-6-5-4-3-2-1 0 1 2 3 4 4 5 6 7 -1 2 C B -3 4 F 5 E -6 -7
Identify the type of line that references point \(E\) and contains point \(F\).Use the graph for the following exercise y 7 6 5 A 4 3 2 D 1 X -7-6-5-4-3-2-1 0 1 2 3 4 4 5 6 7 -1 2 C B -3 4 F 5 E -6 -7
Determine \(\overline{A B} \cup \overline{B D}\).Use the line for the following exercise. A B C D
Determine \(\overleftarrow{B D} \cap \overline{B C}\).Use the line for the following exercise. A B C D
Determine \(\overleftarrow{B A} \cup \overrightarrow{B D}\).Use the line for the following exercise. A B C D
How can you determine whether two lines are parallel?
How can you determine whether two lines are perpendicular?
Determine if the illustration represents a plane. A B C
\(m \measuredangle=180^{\circ}\)Classify the following angles as acute, right, obtuse, or straight.
\(m \measuredangle=176^{\circ}\)Classify the following angles as acute, right, obtuse, or straight.
\(m \measuredangle=90^{\circ}\)Classify the following angles as acute, right, obtuse, or straight.
\(m \measuredangle=37^{\circ}\)Classify the following angles as acute, right, obtuse, or straight.
Find the measure of \(\measuredangle 1\) and state the reason for your solution.Determine the measure of the angles in the given figure. 5500 7 8 1 31 3. 4 6
Find the measure of \(\measuredangle 3\) and state the reason for your solution.Determine the measure of the angles in the given figure. 5500 7 8 1 31 3. 4 6
Find the measure of \(\measuredangle 5\) and state the reason for your solution.Determine the measure of the angles in the given figure. 7 5500 8 6 1 31 3. 4
Find the measure of the missing angle in the given figure. x 26 65
Find the measure of the missing angle in the given figure. x 23
In the isosceles triangle shown, find the missing angles. X 77
In the figure shown given \(\overline{B E}\) is parallel to \(\overline{C D}\), find \(x\) and \(y\). A A B 4 E 2 x D
Find \(a\) and \(t\) in the given figure. 10 B 14 t 12 S
Identify the regular polygons.
Identify the regular polygons.
Identify the regular polygons.
Find the perimeter of the regular pentagon with side length of \(6 \mathrm{~cm}\).
Find the sum of the interior angles of a regular hexagon.
Find the measure of each interior angle of a regular hexagon.
Find the measurements of each angle in the given figure. (x+12) 152 (5x+1), (9x)
Find the circumference of the circle with radius equal to \(3 \mathrm{~cm}\).
What are the properties of repeated patterns that let them be classified as tessellations?
Explain how the using the transformation of a translation is applied to the movement of this shape starting with point \(A\). A A' A"
Starting with the triangle with vertex \(B\), describe how the transformation in this drawing is achieved. B' B B
Starting with a triangle with a darker face and a lighter back, describe how this pattern came about.
Name the tessellation in the figure shown.
Find the area of the triangle with base equal to \(3 \mathrm{~cm}\) and height equal to \(5 \mathrm{~cm}\).
The area of the sail in the sailboat is \(125 \mathrm{ft}^{2}\). The shortest length is \(10 \mathrm{ft}\). What is the height of the sail? h
Find the area of this parallelogram. 14 cm 112 cm
Find the area of a regular hexagon with side length of 5 and apothem equal to 4.3. 4.3 cmi 5 cm
Find the area of circle with a diameter of 16 in.
Find the area of the shaded region in the given figure. 18 in 4.5 in -22 in-
A round tray sits on top of the dining room table. The radius of the tray is \(15 \mathrm{in}\). What is the area taken up by the tray?
Find the surface area of the equilateral triangular prism shown. 10 cm 8.66 cm 10 cm
Find the surface area of the octagonal prism shown. h = 8 in 1 a = 5 in 4 in
Find the volume of the octagonal prism shown with the apothem equal to \(5 \mathrm{in}\), the side length equal to 4 in, and the height equal to 8 in.
Determine the surface area of the right cylinder where the radius of the base is \(10 \mathrm{~cm}\), and the height is \(5 \mathrm{~cm}\).
Find the volume of the cylinder where the radius of the base is \(10 \mathrm{~cm}\), and the height is \(5 \mathrm{~cm}\).
As an artist, you want to design a cylindrical container for your colored art pencils and another rectangular container for some other tools. The cylindrical container will be 8 inches high with a
Find the lengths of the unknown sides of the \(30^{\circ}-60^{\circ}-90^{\circ}\) triangle shown.. 5. 30 b a
Find the missing lengths of the \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle shown. 10 45 C b 45
Use the Pythagorean theorem to find the missing length in the triangle shown. b 3 35
The sun casts a shadow over the roof of a house that ends \(105 \mathrm{ft}\) from the front door as shown in the figure. How high is the house to the tip of the roof? 105 ft 13
Find the measure of side \(c\) in the given figure. 7.5 cm C 40
Find the measure of side \(x\) in the given figure. 15 m x 18
Find \(\overrightarrow{B C} \cup \overrightarrow{C D}\).Use the figure shown for the following exercises. A B C D
Find \(\overline{A C} \cap \overline{B C}\).Use the figure shown for the following exercises. A B C D
Name the points in the set \(\overrightarrow{B D} \cap \overleftarrow{C A}\)Use the figure shown for the following exercises. A B C D
Given that \(l_{1}\) and \(l_{2}\) are parallel lines, solve the angle measurements for all the angles in the figure shown. 5/6 7/8 1/2 3/120
Find the measure of the vertical angles in the figure shown. (5x+8) (6x-7)
Classify the angle as acute, right, or obtuse: \(79^{\circ}\).
Use the given figure to solve for the angles. (7x+12) (3x+1)
Use the given figure to solve for the angle measurements. (6x+1) (9x+4) (6x-14)
Use the given figure to find the measure of the unknown angles. X 34
Use algebra to find the measure of the angles in the figure shown. (x+10) (x-10) X
The two triangles shown are congruent by what theorem?
The two triangles shown are congruent by what theorem?
The two triangles shown are congruent by what theorem?
Are the two figures shown similar?
Are the two triangles shown similar? 12 16 00 8 6 8 4
Find the scaling factor of the two similar triangles in the given figure. 16 64 3 00 8 8 x
Find the length of \(x\) in the figure shown. 16 64 3 3. 00 8 8 x
Identify the polygons.
Identify the polygons. 1
Identify the polygons.
Find the perimeter of a regular hexagon with side length \(5 \mathrm{~cm}\).
The perimeter of a triangle is 18 in the given figure. Find the length of the sides. 3x 3x+1 2x+1
What is the measure of an interior angle of a regular heptagon?
What is the measure of an interior angle of a regular octagon?
Calculate the measure of each interior angle in the figure shown. (13x+3) (11x+1) 72 (7x+5)
Find the measure of an exterior angle of a regular pentagon.
What is the sum of the measures of the exterior angles of a regular heptagon?
Find the circumference of a circle with radius \(3.2 \mathrm{~cm}\).
Find the diameter of a circle with a circumference of \(35.6 \mathrm{in}\).
In what field of mathematics does the topic of tessellations belong?
Tessellations can have no \( \qquad \) or \( \qquad \) .
What type of transformation moves an object over horizontally by some number of units?
What type of transformation results in a mirror image of the shape?
Which regular polygons will tessellate the plane by themselves?
The sum of the interior angles of the shapes meeting at a vertex is equal to how many degrees?
How would you name this tessellation?
What is the area of a triangle with a base equal to \(5 \mathrm{~cm}\) and a height equal to \(12 \mathrm{~cm}\) ?
If the area of a triangle equals \(24 \mathrm{~cm}^{2}\) and the base equals 8 , what is the height?
Find the area of the parallelogram shown. 20 cm 13 cm
If the area of a trapezoid equals \(\frac{45}{2} \mathrm{~cm}^{2}, b_{1}=3 \mathrm{~cm}\), and the height equals \(h=5 \mathrm{~cm}\), find the length of \(b_{2}\).
Find the area of an octagon if the apothem equals \(10 \mathrm{~cm}\) and the side length is \(12 \mathrm{~cm}\).
The area of a circle is \(50.3 \mathrm{in}^{2}\). What is the radius?

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