Exam 7: Applications of Trigonometric Functions

Solve the problem. -A ladder leans against a building that has a wall slanting away from the ladder at an angle of 96° with the ground. If the bottom of the ladder is 23 feet from the base of the wall and it reaches a point 52 feet up the wall, How tall is the ladder to the nearest foot?

Graph the damped vibration curve for 0 $0 \leq t \leq 2 \pi$ . -An object of mass m attached to a coiled spring with damping factor b is pulled down a distance a from its rest position and then released. Assume the positive direction of the motion is up and the period of the first oscillation is T. Write an equation that relates the distance d of the object from its rest position after t seconds. m = 15 g; a = 11 cm; b = 0.7 g/sec; T = 3 sec

Solve the triangle. Find the angles α and β first. - $\mathrm { a } = 8 , \mathrm {~b} = 6 , \mathrm { c } = 4$

Find the area of the triangle. If necessary, round the answer to two decimal places. -Find the area of the shaded portion ( see illustration) of a circle of radius 25 cm, formed by a central angle of 115°. Round your answer to the nearest square cm. [Hint: Subtract the area of the triangle from the area of the sector of the circle to obtain the area of the shaded portion.]

Solve the right triangle using the information given. Round answers to two decimal places, if necessary. - $a = 7 , b = 4 ;$ Find $c , \alpha$ , and $\beta$ .

Solve the right triangle using the information given. Round answers to two decimal places, if necessary. - $a = 5 , \alpha = 25 ^ { \circ }$ ; Find $b , c$ , and $\beta$ .

The displacement d (in meters) of an object at time t (in seconds) is given. Describe the motion of the object. What is the maximum displacement from its resting position, the time required for one oscillation, and the frequency? - $d = 4 \cos ( 5 t )$

Solve the problem. -An airplane is sighted at the same time by two ground observers who are 5 miles apart and both directly west of the airplane. They report the angles of elevation as 14° and 24°. How high is the airplane?

Solve the problem. -A ship at sea, the Admiral, spots two other ships, the Barstow and the Cauldrew and measures the angle between them at be 45°. They radio the Barstow and by comparing known landmarks, the distance between the The Admiral and the Barstow is found to be 323 meters. The Barstow reports an angle of 59° between the Admiral and the Cauldrew. To the nearest meter, what is the distance between the Barstow and the Cauldrew?

Solve the problem. - $\csc ^ { 2 } 65 ^ { \circ } - \tan ^ { 2 } 25 ^ { \circ }$

Solve the triangle. -

The displacement d (in meters) of an object at time t (in seconds) is given. Describe the motion of the object. What is the maximum displacement from its resting position, the time required for one oscillation, and the frequency? - $d = 6 \sin ( 5 t )$

Solve the problem. -A room in the shape of a triangle has sides of length 8 yd, 10 yd, and 14 yd. If carpeting costs $12.50 a square yard and padding costs $4.25 a square yard, how much to the nearest dollar will it cost to carpet the room, Assuming that there is no waste?

Solve the triangle. -

Solve the problem. -A radio transmission tower is 210 feet tall. How long should a guy wire be if it is to be attached 13 feet from the top and is to make an angle of 20° with the ground? Give your answer to the nearest tenth of a foot.

the motion is simple harmonic with period T, write an equation that relates the displacement d of the object from its rest position after t seconds. Also assume that the positive direction of the motion is up.An object attached to a coiled spring is pulled down a distance a from its rest position and then released. Assuming that - $\mathrm { a } = 10 ; \quad \mathrm { T } = 3 \pi$ seconds

Solve the problem. -Two hikers on opposite sides of a canyon each stand precisely 525 meters above the canyon floor. They each sight a landmark on the canyon floor on a line directly between them. The angles of depression from each hiker To the landmark meter are 37° and 21°. How far apart are the hikers? Round your answer to the nearest whole Meter.

The displacement d (in meters) of an object at time t (in seconds) is given. Describe the motion of the object. What is the maximum displacement from its resting position, the time required for one oscillation, and the frequency? - $d = 8 + 2 \sin ( 2 \pi t )$

Find the area of the triangle. If necessary, round the answer to two decimal places. -a = 13, b = 15, c = 13

Solve the triangle. - $\beta = 40 ^ { \circ } , \quad \gamma = 10 ^ { \circ } , \quad \mathrm { b } = 5$