Question

One leg of a right triangle measures 6 inches. The remaining leg measures 6√3 inches. What is the measure of the angle opposite the leg that is 6 inches long?

Answer 1

30°
Here's why:
Using the well-known Pythagorian theorem we can reckon how long the hypotenuse is:
c^2=6^2+36*3 -> c=12
Knowing that sin(a)=a/c=6/12=0.5 the measure of the angle in degrees is 30°
Hope could help :)

Answer 2

30°

Explanation:

One leg of a right triangle measures 6 inches.

Leg 1 (Opposite) = 6

The other leg measure
`6√(3)` inches.

Leg 2 (Base ) =
`6√(3)`

Let the measure of angle opposite of the leg 6 inches be Ф

Using trigonometry identity

`\tan\theta=\frac{\text{Opposite}}{\text{Base}}`

`\tan\theta=(6)/(6√(3))`

Cancel 6 from top and bottom

`\tan\theta=(1)/(√(3))`

`\theta=\tan^(-1)((1)/(\sqrt3))`

`\theta=30^\circ`

Hence, The measure of opposite angle of leg 6 inches is 30°