SOLUTION: If I have a right triangle where the inside angle is 22 degrees and one side is 8 feet long, what are the dimensions of the other two sides??? This has a real world application!!

Question 439431: If I have a right triangle where the inside angle is 22 degrees and one side is 8 feet long, what are the dimensions of the other two sides??? This has a real world application!!
Thanks,
Rich
rjprod@cox.net
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
If I have a right triangle where the inside angle is 22 degrees and one side is 8 feet long, what are the dimensions of the other two sides??? This has a real world application!!
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You did not specify whether the 8 ft side was opposite or adjacent to the 22 deg angle, so you have two different solutions.
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side opposite 22 deg angle=8 ft
other acute angle=90-22=68 deg
let x=other leg opposite the 68 deg angle
let h=hypotenuse (third side)
sin 22/8=sin 68/x
x=8 sin 68/sin 22=19.8
8/h=sin 22
h=8/sin 22=21.36
ans: sides are 8 ft,19.8 ft and 21.36 ft
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side opposite 68 deg angle=8 ft
other acute angle=90-68=22 deg
let x=other leg opposite the 22 deg angle
let h=hypotenuse (third side)
sin 22/x=sin 68/8
x=8 sin 22/sin 68=3.23
8/h=sin 68
h=8/sin68=8.62
ans: sides are 8 ft,3.23 ft and 8.62 ft
..
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