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

Answer:

Option A -- 30 degrees.

Step-by-step explanation:

Knowing two legs of the triangle, 6 and $6\sqrt{3}$, 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

Answer:

∅ = 30°

Step-by-step explanation:

given data

side 1 = 6 inches

side 2 = $6\sqrt{3}$  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∅ = $\frac{perpendicular}{hypotenuse}$     ................2

put here value and we get

put here value and we get

sin∅ = $\frac{6}{12}$  

∅ = $sin^{-1}(0.5)$  

solve it we get

∅ = 30°