SOLUTION: if a gate is 24 inches wide by 46 inches high what are the angles at the angle brace from corner to corner

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Question 411721: if a gate is 24 inches wide by 46 inches high what are the angles at the angle brace from corner to corner
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
given:
a=24in
b=46in
first find hypothenuse c... use Pythagorean Theorem
c=sqrt%2824%5E2%2B46%5E2%29
c=sqrt%28576%2B2116%29
c=sqrt%282692%29
c=51.9

use Trigonometric Identities to find angles:

sin%28A%29+=+a+%2F+c

sin%28A%29+=+24+%2F+51.9+

sin%28A%29+=+0.46

A+=+0.48radians

A+=+27.39 degrees


sin%28A%29%2Fa+=+sin%28B%29%2Fb.....solve for sin%28B%29


.46%2F24+=+sin%28B%29%2F46


%28.46%2F24%2946+=+sin%28B%29

0.8817+=+sin%28B%29

B=1.0758622 radians

B=61.642365 degrees