Question

find the measure of each acute angle in a right triangle where the measure of one acute angle is 8 times the measure of the other acute angle.the smaller acute angles measures $\degree$ and the larger acute angle measures $\degree$ .

Answer 1

• smaller: 10°
• larger: 80°

Explanation:

You want the acute angles in a right triangle in which the larger is 8 times the smaller.

Ratio

The ratio of the acute angles in the triangle is 1 : 8, so the smaller one is 1/(1+8) = 1/9 of the sum of the two angles.

The sum of the acute angles in a right triangle is 90°, so the smaller one is ...

(1/9)(90°) = 10°

The larger is 8 times that:

8 × 10° = 80°

The smaller angle is 10°; the larger angle is 80°.

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