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?

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Answer 1 · 2018-02-25T13:10:41

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.

Given $ˆ R = 40^{\circ}, ˆ S = 120^{\circ}, ˆ T = 20^{\circ}$ $hat R = 40^@, hatS = 120^@,hat T = 20^@$

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$\frac{r}{sin R} = \frac{s}{sin S} = \frac{t}{sin T}$ $r / sin R = s / sin S = t / sin T$

$s = \frac{r sin S}{sin R} = \frac{r sin 120}{sin 40} = 1.3473 r$ $s = (r sin S) / sin R = (r sin 120) / sin 40 = 1.3473 r$

$t = \frac{r sin T}{sin R} = \frac{r sin 20}{sin 40} = 0.5321 r$ $t = (r sin T) / sin R = (r sin 20) / sin 40 = 0.5321r$

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

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.