Question

Find the indicated missing measurement. Include the second solution if applicable. What am I doing wrong?

Answer 1

So this is what I have so far:

sinA/a = sinB/b
sin34 degrees/9 = sinB/7 sinB = 7sin34 degrees/9

sinB = 25.8 degrees... Angle A is less than 90 degrees -> a is greater than or equal to bsinA
bsinA = 7sin34 = 3.91
a is greater than or equal to bsinA = 2 solutions

B' = 180-25.8 = 154.2 degrees

But when I find for angle C of the second triangle it doesn't add up to 180... What am I doing wrong?

Answer 2

\[\frac{\sin 34}{9}=\frac{\sin B}{7}\]
\[\sin B=\frac{7\sin 34}{9}=.4349278\]
B=25.78

Answer 3

C=180-25.78-34=120.22

Answer 4

don't I have to subtract 25.8 from 180 to get the angle of B'?

Answer 5

There is nothing ambiguous about this problem because of the given information. You know that angle B is less than angle A because the side opposite angle B is less than the side opposite angle A. After you find A, use the fact that the sum of the angles of a triangle is 180

Answer 6

sin B = (7 * sin 34 degrees)/9 = 0.4349
\[B=\sin^{-1} 0.4349=25.8degrees\]
C = 180 degrees - (25.8 + 34) = 120.2 degrees
\[\frac{a}{\sin A}=\frac{c}{\sin C}\]
\[\frac{9}{\sin A}=\frac{c}{\sin 120.2}\]
c = 13.9

Answer 7

The second solution is not applicable.

Answer 8

In other words, there is no B' in this problem.

Answer 9

ohhh.. thank you guys!!

Answer 10

yw

Answer 11

but.. wait.

Answer 12

when do I use sine law ambiguous case then?

Answer 13

because isn't angle A an acute angle? Therefore a>b = 1 ohh..

Answer 14

a is greater than b... which means one solution.