Use the law of cosines to find the values of x and y 1219y20o.to

The law of cosines say that cos C=a2+b2-c22ab. Here, in the given triangle x=12,y=19 and z=20.…

Answered: 19 12 to y° 20

Math

Geometry

19 12 to y° 20

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.2: Arithmetic Sequences

Problem 54E

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Question

Use the law of cosines to find the values of x and y

Expert Solution

Step 1

The law of cosines say that $\cos C = \frac{a^{2} + b^{2} - c^{2}}{2 a b}$ .

Here, in the given triangle $x = 12, y = 19 a n d z = 20$ .

Evaluate $x °$ as follows.

$\cos x ° = \frac{y^{2} + z^{2} - x^{2}}{2 y z} \cos x ° = \frac{19^{2} + 20^{2} - 12^{2}}{2 (19) (20)} \cos x ° = \frac{617}{760} \cos x ° = 0.811842105 x ° = \cos^{- 1} (0.811842105) x ° \approx 35.72 °$

Therefore, the value of $x °$ is $35.72 °$ .

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