contestada

Find the measure of each acute angle in a right triangle where the measure of one acute angle is twice the difference of the measure of the other acute angle and 12.

The smaller acute angle measures
$\degree$ and the larger acute angle measures
$\degree$ .

Respuesta :

sqdancefan

Answer:

  • smaller: 38°
  • larger: 52°

Step-by-step explanation:

You want the measures of the acute angles in a right triangle when one is twice the difference of the other and 12.

Angles

Let x represent one acute angle. Then the other is (90 -x) and the relationship between them is ...

  x = 2((90 -x) -12) . . . . . one is twice the difference of the other and 12

  x = 2(78 -x) . . . . . . . . simplify inside parentheses

  3x = 156 . . . . . . . . . . add 2x

  x = 52 . . . . . . . . . . . divide by 3

  90-x = 38 . . . . . . . find the other angle

The smaller angle is 38°; the larger angle is 52°.

Otras preguntas