Exam 8: Triangle Trigonometry and Polar Coordinates

If $\tan \theta=3.271$ , find $\theta$ in degrees. Round to the nearest degree.

If $A=29^{\circ}$ and $a=2$ , find exact values for $b$ and $c$ .

Find the area of the triangle if $a=6, b=12$ , and $B=13^{\circ}$ . Round to two decimal places.

Find the area of the following triangle if $a=13, b=10$ , and $A=87^{\circ}$ . Round to two decimal places.

Use the figure below to find side $b$ when $A=65^{\circ}, B=49^{\circ}$ , and $c=12$ . Round to 2 decimal places.

Consider the triangle formed by the points $A(1,0), B(0,0)$ , and $C(7,4)$ . Find the measure of angle $A B C$ . Give your answer to 2 decimal places.

A 69 inch tall man casts a 101 inch long shadow. What is the angle $\theta$ of the sun? Give your answer to 3 decimal places.

Use the figure below to find the missing side, $c$ , when $a=7, b=4$ , and $C=42^{\circ}$ . Round to 4 decimal places.

Find the area of the triangle if $a=6, b=9$ , and $c=5$ . Round to two decimal places.

If $a=8$ and $b=2$ , find the following. Give your answers to 3 decimal places. A)c B)A C)B

A rope is attached to the top of a tree and to a stake in the ground. The angle of the rope with the ground is $33^{\circ}$ and the rope comes out 150 feet from the tree. How tall is the tree? Give your answer correct to 2 decimal places.

An ant walks up a ramp at an incline of $11^{\circ}$ . If, after 2 minutes, his vertical distance from the ground is 14 inches, how far has the ant traveled in the horizontal direction? Round your answer to 2 decimal places.

Find $A$ and $c$ if $a=7, b=13$ , and $B=12^{\circ}$ . Round to two decimal places.

If $\cos \theta=0.407$ , find $\theta$ in degrees. Round to the nearest degree.

Two airplanes are headed toward the same airport. The first plane is flying $151 \mathrm{mph}$ and the second plane is flying $134 \mathrm{mph}$ . The angle between the planes with its vertex at the airport is $59^{\circ}$ . If both planes reach the airport in 2 hours, how many miles apart are they now? Round to 2 decimal places.

Let $A(1,0), B(0,0)$ , and $C(8,3)$ . Find the area of triangle $A B C$ .

Find the measures of the angles of the triangle if $a=6, b=8$ , and $c=4$ . Round to two decimal places.

Find the following exactly using the figure given if $a=2$ and $c=13$ . 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) $\tan B^{\circ}$

A ramp is 109 feet long and the change in height of the ramp is 4 feet. What angle does the ramp form with the horizontal? Give your answer correct to 3 decimal places.

If $A=29^{\circ}, B=61^{\circ}$ , and $c=7$ , find exact values for $a$ and $b$ . Express your answers in terms of $\sin$ and $\cos$ .