The length of the shorter leg of a 30°-60°-90° triangle is equal to 6 inches. What is the length of its hypotenuse
Cos(30deg)=adjacent/hyp
Cos(30)=6in/hyp
Hyp=6in/cos(30)=
sin 30 = 1/2
2*6 = 12
To find the length of the hypotenuse of a 30°-60°-90° triangle, we can make use of the following relationships:
- The longer leg is equal to the shorter leg multiplied by √3.
- The hypotenuse is equal to twice the shorter leg.
In this case, we are given that the length of the shorter leg is 6 inches. Now we can use these relationships to find the length of the hypotenuse.
First, let's find the length of the longer leg. We can do this by multiplying the length of the shorter leg by √3:
Longer leg = Shorter leg * √3
Longer leg = 6 inches * √3
Longer leg ≈ 10.392 inches (rounded to three decimal places)
Next, we can find the length of the hypotenuse by multiplying the length of the shorter leg by 2:
Hypotenuse = Shorter leg * 2
Hypotenuse = 6 inches * 2
Hypotenuse = 12 inches
Therefore, the length of the hypotenuse of the 30°-60°-90° triangle is 12 inches.