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mathematics
precalculus

Questions and Answers of Precalculus

Completed in 1902 in New York City, the Flatiron Building is triangular shaped and bounded by 22nd Street, Broadway, and 5th Avenue. The building measures approximately 87 feet on the 22nd Street
To approximate the area of a lake, a surveyor walks around the perimeter of the lake, taking the measurements shown in the illustration. Using this technique, what is the approximate area of the
Consult the figure, which shows a circle of radius r with center at O. Find the area K of the shaded region as a function of the central angle θ.
Find the area of the shaded region enclosed in a semicircle of diameter 10 inches. The length of the chord PQ is 8 inches. R. 10
The dimensions of home plate at any major league baseball stadium are shown. Find the area of home plate. 12 in. 12 in. 8.5 in. 8.5 in. 17 in.
A cone-shaped tent is made from a circular piece of canvas 24 feet in diameter by removing a sector with central angle 100° and connecting the ends.What is the surface area of the tent?
The dimensions of a triangular lot are 100 feet by 50 feet by 75 feet. If the price of such land is $3 per square foot, how much does the lot cost?
Find the area of the segment of a circle whose radius is 5 inches, formed by a central angle of 40°.
Find the area of the segment (shaded in blue in the figure) of a circle whose radius is 8 feet, formed by a central angle of 70°. Subtract the area of the triangle from the area of the sector to
Find the area of triangle. Round answers to two decimal places.B = 10°, C = 100°, b = 2
Find the area of triangle. Round answers to two decimal places.A = 110°, C = 30°, c = 3
Find the area of triangle. Round answers to two decimal places.A = 70°, B = 60°, c = 4
Find the area of triangle. Round answers to two decimal places.B = 70°, C = 10°, b = 5
Find the area of triangle. Round answers to two decimal places.A = 50°, C = 20°, a = 3
Find the area of triangle. Round answers to two decimal places.A = 40°, B = 20°, a = 2
Prove the two other forms of the formula given in Problem 25.Data from problem 25If two angles and the included side are given, the third angle is easy to find. Use the Law of Sines to show that the
If two angles and the included side are given, the third angle is easy to find. Use the Law of Sines to show that the area K of a triangle with side a and angles A, B, and C is a? sin B sin C K %3| 2
Find the area of triangle. Round answers to two decimal places.a = 4, b = 3, c = 6
Find the area of triangle. Round answers to two decimal places.a = 5, b = 8, c = 9
Find the area of triangle. Round answers to two decimal places.a = 3, b = 3, c = 2
Find the area of triangle. Round answers to two decimal places.a = 2, b = 2, c = 2
Find the area of triangle. Round answers to two decimal places.a = 4, b = 5, c = 3
Find the area of triangle. Round answers to two decimal places.a = 12, b = 13, c = 5
Find the area of triangle. Round answers to two decimal places.b = 4, c = 1, A = 120°
Find the area of triangle. Round answers to two decimal places.a = 3, c = 2, B = 110°
Find the area of triangle. Round answers to two decimal places.a = 6, b = 4, C = 60°
Find the area of triangle. Round answers to two decimal places.b = 1, c = 3, A = 80°
Find the area of triangle. Round answers to two decimal places.a = 2, c = 1, B = 10°
Find the area of triangle. Round answers to two decimal places.a = 3, b = 4, C = 40°
Find the area of triangle. Round answers to two decimal places. 4 3 4
Find the area of triangle. Round answers to two decimal places. 9, 4
Find the area of triangle. Round answers to two decimal places. 8 4
Find the area of triangle. Round answers to two decimal places. 6 5 8
Find the area of triangle. Round answers to two decimal places. 2 20° 5
Find the area of triangle. Round answers to two decimal places. 95° 3 2.
Find the area of triangle. Round answers to two decimal places. 3 a 30° 4
Find the area of triangle. Round answers to two decimal places. 2 45° 4
True or FalseHeron’s formula is used to find the area of SSS triangles.
The area K of a triangle with sides a, b, and c is K = ___________ where s = _____________.
If two sides a and b and the included angle C are known in a triangle, then the area K is found using the formula K = _______.
The area K of a triangle, whose base is b and whose height is h is ________.
Use the Law of Cosines to prove the identity a + b? + c? 2abc cos A cos B b cos C
For any triangle show thatwhere (s - a)(s – b) sin= ab (a + b + c).
For any triangle, show thatwhereUse a Half-angle Formula and the Law of Cosines. s(s – c) cos 2 ab || (a + b + c).
Show that the length d of a chord of a circle of radius r is given by the formulawhere θ is the central angle formed by the radii to the ends of the chord. See the figure. Use this result to derive
Rod OA rotates about the fixed point O so that point A travels on a circle of radius r. Connected to point A is another rod AB of length L > 2r, and point B is connected to a piston. See the
Clint is building a wooden swing set for his children. Each supporting end of the swing set is to be an A-frame constructed with two 10-foot-long 4 by 4s joined at a 45° angle. To prevent the swing
The distance from home plate to the fence in dead center at the Oak Lawn Little League field is 280 feet. How far is it from the fence in dead center to third base?The distance between the bases in
The distance from home plate to the fence in dead center in Wrigley Field is 400 feet (see the figure). How far is it from the fence in dead center to third base? 400 ft 90 ft 90 fl
A radio tower 500 feet high is located on the side of a hill with an inclination to the horizontal of 5° See the figure. How long should two guy wires be if they are to connect to the top of the
The height of a radio tower is 500 feet, and the ground on one side of the tower slopes upward at an angle of 10° (see the figure).(a) How long should a guy wire be if it is to connect to the top of
According to Little League baseball official regulations, the diamond is a square 60 feet on a side. The pitching rubber is located 46 feet from home plate on a line joining home plate and second
A Major League baseball diamond is actually a square 90 feet on a side. The pitching rubber is located 60.5 feet from home plate on a line joining home plate and second base.(a) How far is it from
In attempting to fly from Chicago to Louisville, a distance of 330 miles, a pilot inadvertently took a course that was 10° in error, as indicated in the figure. (a) If the aircraft maintains an
A cruise ship maintains an average speed of 15 knots in going from San Juan, Puerto Rico, to Barbados, West Indies, a distance of 600 nautical miles.To avoid a tropical storm, the captain heads out
An airplane flies due north from Ft. Myers to Sarasota, a distance of 150 miles, and then turns through an angle of 50° and flies to Orlando, a distance of 100 miles. See the figure.(a) How far is
A golfer hits an errant tee shot that lands in the rough.A marker in the center of the fairway is 150 yards from the center of the green.While standing on the marker and facing the green, the golfer
Solve triangle using either the Law of Sines or the Law of Cosines.a = 10, b = 10, c = 15
Solve triangle using either the Law of Sines or the Law of Cosines.b = 5, c = 12, A = 60°
Solve triangle using either the Law of Sines or the Law of Cosines.A = 65°, B = 72°, b = 7
Solve triangle using either the Law of Sines or the Law of Cosines.A = 10°, a = 3, b = 10
Solve triangle using either the Law of Sines or the Law of Cosines.a = 4, c = 5, B = 55°
Solve triangle using either the Law of Sines or the Law of Cosines.B = 35°, C = 65°, a = 15
Solve triangle using either the Law of Sines or the Law of Cosines.a = 14, b = 7, A = 85°
Solve triangle using either the Law of Sines or the Law of Cosines.a = 6, b = 8, c = 9
Solve triangle using either the Law of Sines or the Law of Cosines.A = 50°, B = 55°, c = 9
Solve triangle using either the Law of Sines or the Law of Cosines.B = 20°, C = 75°, b = 5
Solve each triangle.a = 9, b = 7, c = 10
Solve each triangle.a = 10, b = 8, c = 5
Solve each triangle.a = 4, b = 3, c = 6
Solve each triangle.a = 5, b = 8, c = 9
Solve each triangle.a = 3, b = 3, c = 2
Solve triangle.a = 2, b = 2, c = 2
Solve the triangle.a = 5, b = 8, c = 9
Solve the triangle.a = 12, b = 13, c = 5
Solve the triangle.a = 3, c = 2, B = 90°
Solve the triangle.a = 2, b = 2, C = 50°
Solve the triangle.b = 4, c = 1, A = 120°
Solve the triangle.a = 3, c = 2, B = 110°
Solve the triangle.a = 6, b = 4, C = 60°
Solve each triangle.b = 1, c = 3, A = 80°
Solve the triangle.a = 2, c = 1, B = 10°
Solve the triangle.a = 3, b = 4, C = 40°
Solve triangle. 3 4.
Solve triangle. 9 9. A 4
Solve triangle. B. 4
Solve triangle. 6. A 8
Solve triangle. 2 20° A.
Solve triangle. 950 3 в 2.
Solve triangle. 3 a 30° 4.
Solve the triangle. 2 45° 4
True or FalseA special case of the Law of Cosines is the Pythagorean Theorem.
True or FalseGiven two sides and the included angle, the first thing to do to solve the triangle is to use the Law of Sines.
True or FalseGiven only the three sides of a triangle, there is insufficient information to solve the triangle.
If two sides and the included angle of a triangle are given, the Law of _______ is used to solve the triangle.
If one side and two angles of a triangle are given, the Law of _______ is used to solve the triangle.
If three sides of a triangle are given, the Law of __________ is used to solve the triangle.
If θ is an acute angle, solve the equation cos θ = √2/2.
Write the formula for the distance d from P1 = (x1, y1) to P2 = (x2, y2).
Show thatwhere r is the radius of the circle circumscribing the triangle PQR whose sides are a, b, and c, as shown in the figure.Draw thel diameter PP'. Then B = ∠PQR = ∠PP' R, and angle ∠PRP'

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