Two sides of a triangle measure 4 and 13 and the angle at the vertex where those two sides meet measures 100 degrees. What is the measure of thethird side?A O14.2В3.20.30DO12.9

Answered: wo sides of a triangle measure 4 and 13…

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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Question

Two sides of a triangle measure 4 and 13 and the angle at the vertex where those two sides meet measures 100 degrees. What is the measure of the
third side?
A O
14.2
В
3.2
0.30
DO
12.9

Expert Solution

Step 1

$G i v e n t h a t T w o s i d e s o f t r i a n g l e m e a s u r e 4 a n d 13 a n d a n g l e a t v e r t e x w h e r e t h o s e t w o s i d e s m e e t m e a s u r e s 100 ° T o f i n d : t h i r d s i d e o f t r i a n g l e s o l u t i o n : u \sin g \cos i n e f o r m u l a I n a t r i a n g l e \cos B = \frac{a^{2} + c^{2} - b^{2}}{2 a c} w h e r e B = 100 ° a = 13, c = 4 \cos 100 ° = \frac{13^{2} + 4^{2} - b^{2}}{2 (13) (4)} 2 (13) (4) \cos 100 ° = 13^{2} + 4^{2} - b^{2} b^{2} = 13^{2} + 4^{2} - 2 (13) (4) \cos 100 ° b = \sqrt{13^{2} + 4^{2} - 2 (13) (4) \cos 100 °}$