Question

The measurement of angle R is 40, the measurement of angle S is 120, and the measurement of angle T is 20, how do you find the side lengths to those angles?

Answer 1

We cannot find the exact value of the sides, given the measure of angles.

We can only have the proportional values between the sides.

Triangle has infinite solutions.

Explanation:

Given `hat R = 40^@, hatS = 120^@,hat T = 20^@`

`color(white)(aaaaaaaaaa)` Law of Sines

`r / sin R = s / sin S = t / sin T`

`s = (r sin S) / sin R = (r sin 120) / sin 40 = 1.3473 r`

`t = (r sin T) / sin R = (r sin 20) / sin 40 = 0.5321r`

Sides are in the ratio `r : 1.3473r : 0.5321r`

By assigning different values to r, we can get the corresponding measurements of other two sides s,t.

This triangle has infinite number of solutions.