SOLUTION: The measures of the two acute angels of a right triangle are in the ratio 1:4. The measure of the larger acute angle, in degrees, is.

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Question 1183871: The measures of the two acute angels of a right triangle are in the ratio 1:4. The measure of the larger acute angle, in degrees, is.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let the two acute angels be alpha and beta
if they are in the ratio 1%3A4, we have
alpha%3Abeta=1%3A4........solve for beta
beta=4alpha.........eq.1
if alpha and beta are two acute angels of a right triangle, their sum is 90°
alpha+%2B+beta=90.........eq.2
substitute beta from eq.1
alpha%2B4alpha=90
5alpha=90
alpha=90%2F5
highlight%28alpha=18%29°
then
beta=4%2A18
highlight%28beta=72%29°