SOLUTION: Find the width(a) and height(b) of a right triangle. c = 37". Width to height is a 16:9 ratio.

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Question 169382: Find the width(a) and height(b) of a right triangle. c = 37". Width to height is a 16:9 ratio.
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
Okay, let us illustrate the triangle:

We know the Ratio=width%2Fheight=a%2Fb=16%2F9
By Ratio we get, a=%2816%2F9%29b ------------------> eqn 1
.
Consider the Sides of the Triangle, By Pyth.Theorem:
c%5E2=a%5E2%2Bb%5E2 -------> eqn 2
Subst. eqn 1 in eqn 2:
37%5E2=%28%2816%2F9%29%28b%29%29%5E2%2Bb%5E2
1369=%28256%2F81%29b%5E2%2Bb%5E2
1369=3.1605b%5E2%2Bb%5E2=4.1605b%5E2
cross%281369%29329.047%2Fcross%284.1605%29=cross%284.1605%29b%5E2%2Fcross%284.1605%29
b=sqrt%28329.047%29
highlight%28b=18.14inches%29, Height
Go back eqn 1:
a=%2816%2F9%29%2818.14%29=highlight%2832.25inches=a%29, Width
.
Checking by the Ratio=16%2F9
a%2Fb=32.25%2F18.14=1.7778 ------> 16%2F9=1.7777778; Close enough I guess
Rewriting the Traingle:

.
thank you,
Jojo