Question

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.

Answer 1

The answer to your question is:

acute angle = 54°

legs 7 m y 9.7 m

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

Answer 2

Two legs are 7.0534230 and 9.708203932.

The acute angle is 54 degrees.

Explanation:

For the legs, you can use these two formulas:

12*cos(36)

12*sin(36)

(Make sure you put the 36 in degrees)

For the acute angle, 90-54=36 degrees.