In a right triangle, the length of the hypotenuse is 12m and the measure of one of the acute angles is 36°. Find the measure of the other acute angle and the lengths of the legs.

The answer to your question is:

acute angle = 54°

legs 7 m y 9.7 m

Step-by-step explanation:

Data

Hypotenuse = 12 m

acute angle = 36° = a

acute angle 2 = ? = b

lengths of legs=?

Process

The sum of the internal angles on a triangle equals 180°

a + b + 90 = 180

36 + b + 90 = 180

b = 180 - 126

b = 54°

sin Ф = opposite leg / hypotenuse

opposite leg = hypotenuse x sin Ф

opposite leg = 12 x sin 36

opposite leg = 7 m

Pythagorean theorem

c² = a² + b²

a² = c² - b²

a² = 12² - 7²

a² = 144 - 49

a ² = 95

a = 9.7 m