please help!! #12Given right triangle QRS below, do the following:(a) Determine the length of side QS. [2 points]48S.55(b) Determine the measure of ZS to the nearest degree. [2 points]1 Add file+12

Name: please help!! #12Given right triangle QRS below, do the following:(a)
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Description: please help!! #12Given right triangle QRS below, do the following:(a) Determine the length of side QS. [2 points]48S.55(b) Determine the measure of ZS to the nearest degree. [2 points]1 Add file+12

Answered: Given right triangle QRS below, do the…

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Additional Topics In Trigonometry

Section3.1: Law Of Sines

Problem 60E

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please help!!

#12
Given right triangle QRS below, do the following:
(a) Determine the length of side QS. [2 points]
48
S.
55
(b) Determine the measure of ZS to the nearest degree. [2 points]
1 Add file
+12

Expert Solution

Step 1

(a)

The given triangle $Q R S$ is right angled triangle, so, apply Pythagorean theorem as follows:

${(Q S)}^{2} = {(Q R)}^{2} + {(R S)}^{2}$ [Note the side opposite to $90 °$ angle is hypotenuese]

$\Rightarrow {(Q S)}^{2} = 48^{2} + 55^{2}$

$\Rightarrow {(Q S)}^{2} = 2304 + 3025$

$\Rightarrow {(Q S)}^{2} = 5329$

$\Rightarrow Q S = 73$

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