Exam 6: Trigonometric Functions: Right Triangle Approach

A car travels along a straight road, heading west for three hours, and then travels northeast on another road for two hours. If the car has maintained a constant speed of $55$ mi/h, how far is it from its starting position?

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

Find all angles $\theta$ between $0$ and $180 ^ { \circ }$ satisfying the given equation. $\sin \theta = \sqrt { 2 } / 2$

Use Heron's formula to find the area of the triangle with sides of length 10, 12, and 20.

Find the reference angle for $\theta = 139 ^ { \circ }$

From the top of a $250$ ft lighthouse, the angle of depression to a ship in the ocean is $18 ^ { \circ }$ . How far is the ship from the base of the lighthouse?

A 12-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?

Sketch the triangle given by $\angle A = 23 ^ { \circ }$ , $\angle B = 78 ^ { \circ }$ , $c = 88$ , and solve it using the Law of Sines.

To find the distance across a river a surveyor chooses points $A$ and $B$ , $50$ 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 $\angle A = 54 ^ { \circ }$ and $\angle B = 77 ^ { \circ }$ .

Find the degree measures that correspond to the radian measures $- 3 \pi / 5$ and $3.1$ .

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

A 86-ft tree casts a shadow that is 110 ft long. What is the angle of elevation of the sun?

Find the area of the shaded region.

A girl is flying two kites at the same time. If the strings are $200$ ft and $230$ ft long and the kites are $100$ ft apart, what angle do the strings make in her hands?

Find the angle $\theta$ in the triangle.

Find the values of the trigonometric functions of $\theta$ given that $\cot \theta = - \frac { 4 } { 3 }$ and $\text { sect } > 0$ .

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

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

Use the Law of Cosines to find $x$ .

Find all angles $\theta$ between $0$ and $180 ^ { \circ }$ satisfying the given equation. $\cos \theta = 0.9$