Question

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

30°
45°
60°
90°

Answer 1

Option A -- 30 degrees.

Explanation:

Knowing two legs of the triangle, 6 and
`6√(3)`, we know that this is a 30-60-90 triangle since the measurements match the requirements. Therefore, the last angle is 30 degrees.

Answer 2

∅ = 30°

Explanation:

given data

side 1 = 6 inches

side 2 =
`6√(3)` inches

to find out

angle opposite the leg that is 6 inches long

solution

we will use pythagoras theorem that is express as

hypotenuse² = perpendicular² + base² .......................1

put here value and we get hypotenuse

hypotenuse² = 6² + ( )²

solve it we get

hypotenuse² = 144

hypotenuse = 12 inches

now we apply here sin∅ that is

sin∅ =
`(perpendicular)/(hypotenuse)` ................2

put here value and we get

put here value and we get

sin∅ =
`(6)/(12)`

∅ =
`sin^(-1)(0.5)`

solve it we get

∅ = 30°