SOLUTION: I need to find angles and sides for this right triangle but I dont know how and cant find any examples anywhere to help(I don't know how because of angle A) Find side a and b give

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Question 140509: I need to find angles and sides for this right triangle but I dont know how and cant find any examples anywhere to help(I don't know how because of angle A)
Find side a and b given in two decimal place and find Angle A is Pi/10 and side c is 43.8
Please help.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Angles can be measured in different units just like length can be measured in inches and in millimeters (and a lot of other units).
Two commonly used units are degrees and radians.
A circle, like a clock, sweeps 360 degrees.
In radians, it would be 2%28pi%29 radians.
So the conversion factor is 2%28pi%29%2F360 to go from degrees to radians.
The conversion factor to go from radians to degrees is 360%2F%282%28pi%29%29.
The angle A is %28pi%29%2F10 radians or 18 degrees.
Let's call the side oppposite angle A, side b.
Let's call the side adjacent (next to) angle A, side a.
Side c is the hypotenuse of the right triangle.
From trignometry,
sin%28A%29=b%2Fc
b=c%2Asin%28A%29
b=43.8%2Asin%2818%29
b=43.8%2A0.3090
b=13.53
Since it's a right triangle, you can use the Pythagorean theorem to find a.
a%5E2%2Bb%5E2=c%5E2
a%5E2%2B%2813.5%29%5E2=%2843.8%29%5E2
a%5E2%2B183.19=1918.44
a%5E2=1735.25
a=41.66
You could have also use the cos(A).
cos%28A%29=a%2Fc
a=c%2Acos%28A%29
a=43.8%2Acos%2818%29
a=43.8%2A0.9511
a=41.66
a=41.66
b=13.53