Question

In triangle ABC, A=32 degrees, a=8, and b=7. Find C.
A 120.4°
B 110.7°
C 30.4°
D 20.7°

(it think its 110.7 but I'm not sure)

Answer 1

is there a figure for this question?

Answer 2

sin 32/8 = sin b/7 -> Sin B= 7sin32/8

Answer 3

Use the law of sines to first figure out angle B.
a / sin(A) = b / sin(B)
sin(B) = b / a * sin(A)
Plug in the numbers and find B

Then C = 180 - (A + B)

Answer 4

would A be 32?

Answer 5

What do you get for angle B?
sin(B) = 7/8 * sin(32) = ?
Then take the sine inverse to find B.

Answer 6

inverse meaning 8/7?

Answer 7

0.46?

Answer 8

sin(B) = 7/8 * sin(32) = 0.4637 (this is the sine value)
To find angle B you will have to find \(\Large \sin^{-1}(0.4637)\)

Answer 9

That is called the sine inverse.

Answer 10

soooo 36+0.4637-180 = -143?

Answer 11

No. That 0.4637 is the sine value. That is NOT the angle B. It is sin(B).
sin(B) = 0.4637
Find angle B.
B = inverse sine of (0.4637)

In your calculator find how to calculate the inverse sine.

Answer 12

27.6?

Answer 13

Yes. Angle B = 27.6 degrees.

Angle C = 180 - Angle A - Angle B = 180 - 32 - 27.6 = ?

Answer 14

120.4?
'