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

Answer:

 Other acute angle = 54°

 Length of other legs = 9.71 m and 7.05 m.

Explanation:

 We have sine formula

        $\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}$

 B = 90°, C = 36°, b = 12 m

 So, A = 180 - ( 90 + 36 ) = 54°

 Other acute angle = 54°

     $\frac{a}{sin54} =\frac{12}{sin90} =\frac{c}{sin36}\\ \\ \frac{a}{sin54} =\frac{c}{sin36}=12\\ \\ a=12sin54 = 9.71m\\ \\ c=12sin36=7.05m$

Length of other legs = 9.71 m and 7.05 m.