Exam 6: Trigonometric Functions: Right Triangle Approach

A satellite passes over two tracking stations, $A$ and $B$ , $300$ km apart. When the satellite is between the two stations the angles of elevation at the stations are measured as $84.5 ^ { \circ }$ and $88.2 ^ { \circ }$ respectively. What is the distance $a$ , between the satellite and station $B$ .

Find the exact value of the expression. $\sin \left( \cos ^ { - 1 } \frac { 4 } { 5 } \right)$

Solve the triangle. $\angle C = 34 ^ { \circ }$ , $a = 3$ , $b = 2$

How many revolutions will a bicycle wheel of diameter 26 inches make as the bicycle travels a distance of $4$ miles?

Use a calculator to find an approximate value of each expression correct to five decimal places, if it is defined. (a) $\cos ^ { - 1 } ( - 0.25 )$ (b) $\sin ^ { - 1 } ( 3 / 4 )$

Use a calculator to find an approximate value of each expression correct to five decimal places, if it is defined. (a) $\cos ^ { - 1 } ( - 3 / 4 )$ (b) $\sin ^ { - 1 } ( 0.25 )$

At a point $550$ ft from the base of a building, the angles of elevation to the bottom of a radio transmission tower and to the top of the tower are $31 ^ { \circ }$ and $43^ { \circ }$ . Find the height of the radio tower to the nearest foot.

A pilot sets out from an airport and heads in the direction N $30 ^ { \circ }$ W, flying at a constant speed of $305$ mi/h. Forty-five minutes later the pilot makes a course and speed correction and now heads in the direction N $50 ^ { \circ }$ W and reduces her speed to $175$ mi/h. Half an hour later, engine trouble forces her to make an emergency landing. Find the distance between the airport and the final landing point.

Find all angles $\theta$ between $0$ and $180 ^ { \circ }$ satisfying the given equation. $\sin \theta = 0.7$

Find the reference angle for $\theta = - 202$

Solve the triangle. $\angle A = 45 ^ { \circ }$ , $b = 18$ , $c = 24$

A 22-ft ladder leans against a building so that the angle between the ground and the ladder is $72 ^ { \circ }$ . How high does the ladder reach on the building?

Solve the triangle. $\angle B = 67 ^ { \circ }$ , $a = 3.42$ , $c = 2.56$

Find the exact value of the expression. $\csc \left( \cos ^ { - 1 } \frac { 24 } { 25 } \right)$

Use the Law of Cosines to find $\theta$ .

Use a calculator to find an approximate value of each expression correct to five decimal places, if it is defined. (a) $\tan ^ { - 1 } ( 3 )$ (b) $\sin ^ { - 1 } ( - 3 )$

Find an angle between $0$ and $2 \pi$ that is coterminal with each angle given. a. $\frac { 17 \pi } { 2 }$ b. $- \frac { 15 \pi } { 4 }$ c. $85 \pi$

Find the values of the trigonometric functions of $\theta$ given that $\sec \theta = - 2$ and $\tan \theta > 0$ .

Solve the triangle. $\angle B = 88 ^ { \circ }$ , $a = 15$ , $c = 7$

Use the Law of Cosines to find $x$ .