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1Determine the value of a.


2       

Find the length of the missing side of the trapezoid below.

 Mar 27, 2021
 #1
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-3

1. By the sine law, a = 6.

 

2. By the Pythagorean Theorem, the missing side is 5*sqrt(3).

 Mar 27, 2021
 #2
avatar+420 
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1. It's hard to apply the sine rule here. Instead, notice that the length WY is \(4\sqrt2\) , because triangle WXY is a 45-45-90 triangle, and notice that angle WYZ is a right triangle, so to find A, use the Pythagorean theorem:

\(9^2=(4\sqrt2)^2+a^2\\81=32+a^2\\49=a^2\\a=7\)

2. Let x be the missing side. Using the Pythagorean theorem,

\(7^2=(8-5)^2+x^2\\49=9+x^2\\40=x^2\\x=2\sqrt10\)

textot  Mar 27, 2021
edited by textot  Mar 27, 2021
 #3
avatar+336 
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Oh yeah that makes since.

wolfiechan  Mar 27, 2021

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