Oblique Triangles (Law of Sines)

Using the law of sines, which expression is equivalent to  $\frac{b}{\sin\ B}$   ?

•  $\frac{a}{\sin\ A}$  

•  $\frac{a}{c}$  

•  $\frac{\sin\ A}{a}$  

•  $\frac{c}{\sin A\ }$  

In triangle ABC, which expression is equal to b?

• $\frac{\sin\ A}{a\sin B}$

• $\frac{c\ \sin\ B}{\sin\ B}$

• $\frac{a\sin B}{\sin A}$

• $\frac{\sin\ C}{c\ \sin\ B}$

The law of sines cannot be used to solve a triangle if

• three sides are given.

• two angles and a side are given.

• the given triangle is a right triangle.

• two sides and an angle opposite one of them are given.

If we are given sides a and c along with angle A, which of the following can be found by using the law of sines?

• side b

• angle B

• angle C

• side b, angle B and angle C

For any triangle ABC, which of the following is not true?

• $\frac{\sin\ A}{a}=\frac{\sin\ B}{b}$

• $\frac{\sin\ A}{\sin\ B}=\frac{a}{b}$

• $b\sin\ A\ =\ a\ \sin\ B$

• $a\sin\ A\ =\ b\ \sin\ B$

For the given triangle ABC,  $\angle C$  can be found by using the equation 

•  $\sin\ C\ =\ \frac{9}{8}$  

•  $\sin\ C\ =\ \frac{8}{9}$  

•  $\frac{b}{\sin\ 30^0}=\ \frac{9}{\sin\ C}$  

•  $\frac{9}{\sin\ C}=\frac{8}{\sin\ 30^0}$  

How many non-congruent triangles ABC can be formed if c = 5 , A = 60^o , and a = 8?

• none

• one

• two

• three

If you find a missing side using the law of sines, what information do you need?

• all three sides.

• the other two sides.

• another side and opposite angle

• the opposite angle with another side and its opposite angle.

In triangle EFG, if F=95⁰, G=53⁰, and e=12, what is the approximate value of g?

• 8.6

• 15

• 18.1

• 19.2

The shortest side of a triangle with angles 50⁰, 60⁰, and 70⁰ has length of 9 inches. What is the approximate length, in inches, of the longest side?

• 11

• 11.5

• 12

• 12.5