Question 1157781: In ΔRST, angle R = 140° and side s = (3/4)r. Find the measures of angles S and T.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i believe the law of sines is what you need to solve this problem.
the law of sines says:
side s / sine of angle S = side r / sine of angle R.
you are given that side s is equal to 3/4 * side r
the formula becomes:
3/4 * side r / sine of angle S = side r / sine of angle R.
cross multiply to get:
3/4 * side r * sine of angle R = sine of angle S * side r
since angle R is equal to 140 degrees, this equation becomes:
3/4 * side r * sine of 140 degrees = sine of angle S * side r
divide both sides of this equation by side r to get:
3/4 * side r / side r * sine of 140 degrees = sine of angle S.
side r / side r cancels out and you are left with:
3/4 * sine of 140 degrees = sine of angle S.
sine of 140 degrees is equal to .6427876097.
3/4 times that is equal to .4820907073
take the arcsine of that to get angle S equal to 28.82203865 degrees.
since the sum of the angles of a triangle is always equal to 180 degrees, then you get:
angle T is equal to 180 minus 28.82203865 minus 140 = 11.17796135 degrees.
you now have all the angles of the triangle.
angle R = 140 degrees.
angle S = 28.82203865 degrees.
angle T = 11.17796135 degrees.
here's a reference on the law of sines.
https://www.mathopenref.com/lawofsines.html
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