Questions on Geometry: Angles, complementary, supplementary angles answered by real tutors!

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Question 148271: to the nearest tenth of a degree, find the sizes of the acute angles in the right triangle whose hypotenuse is 2.5 times as long as its short leg.: to the nearest tenth of a degree, find the sizes of the acute angles in the right triangle whose hypotenuse is 2.5 times as long as its short leg.
Answer by vleith(1238) About Me  (Show Source):
You can put this solution on YOUR website!
Assume the short side is adjacent to the hypotenuse.
cos(z) = adjacent/hypotenuse = 1/2.5
To find z, use arccosine(1/2.5) = z = 23.6
So one angle is 23.6 degrees and the other one is 180-90-23.6 = 66.4degrees
Question 148271: to the nearest tenth of a degree, find the sizes of the acute angles in the right triangle whose hypotenuse is 2.5 times as long as its short leg.: to the nearest tenth of a degree, find the sizes of the acute angles in the right triangle whose hypotenuse is 2.5 times as long as its short leg.
Answer by Nate(3495) About Me  (Show Source):
You can put this solution on YOUR website!
drawing( 400, 300, -10, 10, -10, 10, triangle( -8, -4, 8, -4, 8, 0 ), locate( 0, -0.5, 2.5x ), locate( 8.5, -1.5, x), locate( -4, -3, O), locate( 7, -0.5, Q ) )
Let's begin with angle O. We need a trig identity that would include the opposite leg and the hypotenuse. _SOH_ CAH TOA
sin O = x / 2.5x
sin O = 1 / 2.5
sin O = 0.4
O = 23.6 degrees
Angle Q = 90 - Angle O
Angle Q = 90 - 23.6
Angle Q = 66.4 degrees