Unit 8 test: Oblique Triangles

In triangle $ABC$, $A = 38^\circ$, $B = 72^\circ$ and $a = 15$. Find $b$ to the nearest tenth.

In triangle $ABC$, $A = 44^\circ$, $C = 68^\circ$ and $b = 25$. Find $a$ to the nearest tenth.

How many triangles have $A = 55^\circ$, $a = 8$ and $b = 12$?

How many triangles have $A = 36^\circ$, $a = 7$ and $b = 10$?

For the triangle data in the previous question ($A = 36^\circ$, $a = 7$, $b = 10$), find all possible values of angle $B$ to the nearest tenth of a degree. Separate answers with a comma.

How many triangles have $A = 120^\circ$, $a = 10$ and $b = 6$?

In triangle $ABC$, $b = 9$, $c = 13$ and $A = 47^\circ$. Find $a$ to the nearest tenth.

A triangle has sides $6$, $8$ and $11$. Find its largest angle to the nearest tenth of a degree.

In triangle $ABC$ you know sides $a$ and $b$ and angle $C$. What is the best first step to solve the triangle?

A triangle has sides $a = 11$ and $b = 16$ with $C = 58^\circ$ between them. Find its area to the nearest tenth.

Use Heron's formula to find the area of a triangle with sides $11$, $13$ and $20$.

To find the distance $AB$ across a lake, a surveyor stands at point $C$ and measures $CA = 320$ m, $CB = 410$ m, and $\angle ACB = 72^\circ$. Find $AB$ to the nearest meter.

Lookout towers $P$ and $Q$ are $12$ miles apart. A signal flare $F$ is sighted at an angle of $48^\circ$ from line $PQ$ at tower $P$ and $63^\circ$ from line $PQ$ at tower $Q$. How far is the flare from tower $P$, to the nearest tenth of a mile?