Question

How many solutions does a triangle with values a=22, A= 117 degrees, and b=34 have? Write your answer in numeric form

Answer 1

0 —- there are zero solutions

Explanation:

Since a<b, you need to find the value of (b/a)sinA. If it’s less than 1, there are 2 solutions. If it’s equal to 1, there is 1 solution. If it is greater than 1, there are 0 solutions.

When you plug in (34/22)sin(117degrees) it should equal about 1.377, which is greater than 1. Therefore, there are no solutions.

Answer 2

The answer to this would be “None” or “0“.

The explanation to this is that the 3 angles in a triangle must sum up to 180 degrees.

Given that angle A is 117 degrees opposite to side a of 22 units, therefore angle B must be greater than 117 degrees since it is opposite to side b of 34 units. The bigger the length of the side, the bigger is the angle opposite to it.

Assuming angle B is 118 degrees (the minimum it can have since it must be bigger than angle A):

sum of 2 angles = 117 degrees + 118 degrees

sum of 2 angles = 235 degrees (Cannot be)