SOLUTION: In a right triangle, a bisector of the right angle divides the hypotenuse in the ratio of 3:5. Determine the measure of the acute angles.

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Question 1007444: In a right triangle, a bisector of the right angle divides the hypotenuse in the ratio of 3:5. Determine the measure of the acute angles.
Answer by MathLover1(20850) About Me  (Show Source):
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In a right triangle, a bisector of the right angle divides the hypotenuse in the ratio of 3:5. Determine the measure of the acute angles.
let the acute angles be alpha and beta
if a bisector of the right angle divides the hypotenuse in the ratio of 3%3A5, then the measures of acute angles be alpha and beta will be in same ratio; so,
alpha%2Fbeta=3%2F5
alpha=%283%2F5%29beta
since alpha%2Bbeta=90, we have
%283%2F5%29beta%2Bbeta=90
%283%2F5%29beta%2B%285%2F5%29beta=90
%288%2F5%29beta=90
beta=90%2F%288%2F5%29
beta=450%2F8
highlight%28beta=56.25%29
now find alpha
alpha=%283%2F5%29beta
alpha=%283%2A56.25%29%2F5
alpha=3%2A11.25
highlight%28alpha=33.75%29