Exam 6: Trigonometric Functions: Right Triangle Approach

Use a calculator to find an approximate value of each expression correct to five decimal places, if it is defined. (a) $\tan ^ { - 1 } ( 2 )$ (b) $\cos ^ { - 1 } ( 2 )$

Land on a small Caribbean island is valued at $\$ 45$ per square foot. What is the value of a triangular lot with sides of lengths $80$ ft, $50$ ft, and $120$ ft?

Find the exact value of each expression, if it is defined. (a) $\cos ^ { - 1 } \left( \frac { \sqrt { 3 } } { 2 } \right)$ (b) $\sin ^ { - 1 } \left( - \frac { 1 } { 2 } \right)$ (c) $\tan ^ { - 1 } ( - 1 )$

To find the distance across a river a surveyor chooses points $A$ and $B$ , $100$ m apart and a reference point $\mathrm { C }$ on the other side of the river. Approximate the distance, $b$ , between $A$ and $\mathrm { C }$ given that $\angle A = 93 ^ { \circ }$ and $\angle B = 62 ^ { \circ }$ .

Use either the Law of Sines or the Law of Cosines to find $\theta$ .

Find the angle $\theta$ in the figure. $9.5 \mathrm {~m}$ 9.5 m 4 m

Find the radian measures that correspond to the degree measures $- 300 ^ { \circ }$ and $135 ^ { \circ }$ .

Find the area of a triangle with sides of lengths $10.5$ ft, $13.2$ ft, and $18$ ft.

Find all angles $\theta$ between $0$ and $180 ^ { \circ }$ satisfying the given equation. $\sin \theta = 1 / 8$

A satellite passes over two tracking stations, $A$ and $B$ , $100$ km apart. When the satellite is between the two stations the angles of elevation at the stations are measured as $89 ^ { \circ }$ and $87 ^ { \circ }$ respectively. What is the distance, $a$ between the satellite and station $B$ .

To estimate the height of a building above a level plain, a surveyor measures the angle of elevation to the top of the building to be $28.5 ^ { \circ }$ . Three hundred feet closer to the building the angle of elevation is $32.5 ^ { \circ }$ . Estimate the height of the building. Round your answer to the nearest foot.

Find the exact value of $\sec ( 14 \pi / 6 )$ .

Solve the triangle. $a = 72.5 , \quad \angle B = 60 ^ { \circ } , \quad \angle C = 83 ^ { \circ }$

Find the length of the arc $s$ in the figure. 5 cm s

Find the length of an arc of a circle of radius 4 km if the arc subtends a central angle of $4$ radians.

Find the radius of a circle in which a sector with central angle 3 radians has an area of $24 \mathrm {~m} ^ { 2 }$ .

Sketch the triangle given by $\angle A = 53 ^ { \circ }$ , $\angle B = 43 ^ { \circ }$ , $c = 50$ , and solve it using the Law of Sines.

Find the area of a sector with central angle $120 ^ { \circ }$ in a circle with radius $12$ m.

Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. $a = 99 , \quad b = 81 , \quad \angle A = 135 ^ { \circ }$

Find the exact value of $\sin ( 19 \pi / 2 )$ .