Holly G.

asked • 07/22/21# Solve the following triangle, rounding answers to the nearest tenth if necessary. In ∆RST, r = 12.6 m, s = 11.5 m, and t = 13.2 m

This is a right triangle, I believe.

## 1 Expert Answer

Yefim S. answered • 07/22/21

Math Tutor with Experience

By cosine law cosT = (r^{2} + s^{2} - t^{2})/(2rs) = (12.6^{2} + 11.5^{2} - 13.2^{2})/(2·12.6·11.5) = .402933;

T = cos^{-1}(.402933) = 66.2°.

By sine law sinS = s·sinT/t = 11.5sin66.2°/13.2 = .7971; S = sin^{-1}(.7971) = 52.9°

R = 180° - (T + S) = 180° - (66.2° + 52.9°) = 60.9°

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Doug C.

Since 11.5^2 + 12.6^2 does not equal 13.2^2 this is not a right triangle. Since the given info is SSS, use the Law of Cosines to find the angle opposite the 13.2 side, then Law of Sines to find the angle opposite 12.6. Finally Triangle Sum Theorem (180 degrees) to find the 3rd angle. Once you have tried the above check out this Desmos graph to confirm your answer: desmos.com/calculator/ojbi93ly72 This graph uses the Law of Cosines to find all three angles, but that is not necessary.07/22/21