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Chapter 7: Problem 15

Solew the given triangles. The standard notation for labeling of triangles is used. Round answers to four decimal places. $$a=4.7, b=8.4, c=5.6$$

Short Answer

Expert verified
Use the respective formulas for each step, plug in the given values, then do the appropriate arithmetic to get the precise measures of angles A, B, and C.

Step by step solution

01

Calculate Angle A

Angle A can be found using the law of cosines formula: \( A = \cos^{-1}\left( \frac{b^2 + c^2 - a^2}{2bc} \right) \). Substituting the given values for a, b, and c, we get: \( A = \cos^{-1}\left( \frac{(8.4)^2 + (5.6)^2 - (4.7)^2}{2 \cdot 8.4 \cdot 5.6} \right) \)
02

Calculate Angle B

Angle B can also be calculated following the same principle as for Angle A: \( B = \cos^{-1}\left( \frac{c^2 + a^2 - b^2}{2ca} \right) \). After substituting the values, we get: \( B = \cos^{-1}\left( \frac{(5.6)^2 + (4.7)^2 - (8.4)^2}{2 \cdot 5.6 \cdot 4.7} \right) \)
03

Calculate Angle C

The sum of interior angles in a triangle is always 180掳. Therefore, we can find the third angle by subtracting the sum of angles A and B from 180掳: \( C = 180掳 - A - B \)

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