Exam 6: Trigonometric Functions: Right Triangle Approach

A $75$ ft tree casts a shadow that is $45$ ft long. What is the angle of elevation of the sun?

Find the exact value of $\cot \left( - 675 ^ { \circ } \right)$ .

Find the radian measures that correspond to the degree measures $- 1080 ^ { \circ }$ and $15 ^ { \circ }$ .

Use the Law of Sines to solve for all possible triangles that satisfy $b = 13$ , $c = 17$ , $\angle B = 43 ^ { \circ }$ .

Solve the triangle. $\angle C = 52 ^ { \circ }$ , $a = 1.54$ , $b = 1.87$

A boy is riding a scooter whose wheels are $5$ inches in diameter. If the wheels rotate at $550$ rpm, find the speed at which he is traveling in mi/h.

Two tugboats are pulling a barge with cables $50$ m and $62$ m long. If the angle between the cables is $33 ^ { \circ }$ approximately how far apart are the barges?

Solve the triangle. $\angle A = 53 ^ { \circ }$ , $b = 11$ , $c = 23$

Solve the triangle using the Law of Sines.

Solve for $x$ correct to one decimal place.

Use the Law of Sines to solve for all possible triangles that satisfy $\angle A = 25 ^ { \circ }$ , $a = 5$ , $b = 8$ .

Find the length of an arc of a circle of radius $3$ m if the arc subtends a central angle of $75 ^ { \circ }$ .  

Two cities, $A$ and $B$ lie on the same meridian, one is found at $20 ^ { \circ }$ S and the other at $27 ^ { \circ }$ S. Find the distance between these cities given that the circumference of the earth is $3960$ mi.

Find the exact value of the expression. $\tan \left( \cos ^ { - 1 } \frac { 5 } { 13 } \right)$

Sketch the triangle given by $\angle A = 113 ^ { \circ }$ , $\angle B = 37 ^ { \circ }$ , $c = 25$ , and solve it using the Law of Sines.

Find the exact value of $\cot ( 18 \pi / 4 )$ .

Find the exact value of $\csc ( - \pi / 3 )$ .

Find the angle $\theta$ in the triangle.

Find the exact value of the expression. $\tan \left( \sin ^ { - 1 } \frac { 3 } { 5 } \right)$