Exam 8: Triangle Trigonometry and Polar Coordinates

Find the area of the triangle given if $c=9$ and $A=37^{\circ}$ . Give your answer correct to 3 decimal places.

In the revolving door in the figure below, each panel is 1 meter long. How many meters is the distance along a straight line between $A$ and $D$ ? Round to 2 decimal places.

If $A=22^{\circ}$ and $c=7$ , find two different expressions for the exact value of $a$ .

In the following figure, suppose $c=1.2, b=2.2$ , and $C=22^{\circ}$ . Find $a$ , and round your answer to two decimal places. If there are two possible answers, list both.

The Pentagon proposes to install a 5 panel revolving door with a panel width of 0.9 meters. A 5-star general wants to enter with a chart that is as wide as possible. How many meters wide is the widest chart that he can fit in the opening without bending it? In other words, how many meters is the distance across the opening? Round to 2 decimal places.

Find the area of a triangle with angles $110^{\circ}, 21^{\circ}$ , and $49^{\circ}$ if the length of the side opposite the $110^{\circ}$ angle is 8 . Round to 2 decimal places.

Find $\sin \theta=60^{\circ}$ exactly.

In the following figure, suppose $c=1.3, b=2.3$ , and $C=23^{\circ}$ . Find $A$ , and round your answer to two decimal places. If there are two possible answers, list both.

Let $c=7$ and $A=28$ , find the following. Give your answers to 3 decimal places. A) $a$ B) $b$ C) $B$

If $\sin \theta=0.993$ , find $\theta$ in degrees. Round to the nearest degree.

Use the figure below to find angle $C$ when $b=13$ , and $c=14$ , and $B=95^{\circ}$ . Round to 2 decimal places. If the triangle is not possible, enter "not possible".

Find the following exactly using the figure given if $a=4$ and $b=5$ . Express your answers as unsimplified radicals when appropriate. A) $\sin A^{\circ}$ B) $\cos A^{\circ}$ C) $\tan A^{\circ}$ D) $\sin B^{\circ}$ E) $\cos B^{\circ}$ F) $\tan B^{\circ}$

Two ships leave port and head out to sea in straight lines at $1 \mathrm{pm}$ . It is noted that they are travelling away from each other at an angle of $41^{\circ}$ . Ship A travels at 15 miles per hour and Ship B travels at 16 miles per hour. After how many hours are they 82 miles apart?

Let $A(1,0), B(3,5)$ , and $C(0,-1)$ . Find the measure of angle $A B C$ . Give your answer to 2 decimal places.

In the figure below, when $a=12, b=9$ , and $C=43^{\circ}$ , we have (A= ---------°). Round to 2 decimal places. If the triangle is not possible, enter "not possible".

To measure the height of a mountain, a person stands a certain distance from the base and measures the angle of elevation to the top of the mountain. This turns out to be $69^{\circ}$ . Moving $100 \mathrm{ft}$ closer, the angle of elevation to the top of the mountain is $74^{\circ}$ . How tall is the mountain? Round your answer to 2 decimal places.

If $a=4$ and $c=7$ , find the following exactly. Express your answers as unsimplified radicals when appropriate. A) $\sin A^{\circ}$ B) $\cos A^{\circ}$ C) $\tan A^{\circ}$

Find $\cos \theta=150^{\circ}$ exactly.

If $a=2$ and $c=7$ , find the following exactly. A) $\sin A^{\circ}$ B) $\cos A^{\circ}$ C) $\tan A^{\circ}$

Let $a=7$ and $A=25^{\circ}$ , find the following. Give your answers to 3 decimal places. A) $c$ B) $b$ C) $B$