Did I do this right?
The shorter leg of a 30°- 60°- 90° right triangle is 7.5 inches. How long is the longer leg and the hypotenuse?
1) The longer side:
7.5/Sin 60 =b/Sin 30
4.208723391 inches
Hypotneuse:
8.6 inches
ARRRRRGGGGGG.
The shorter leg is opposite the smallest angle.
7.5/sin30=longerleg/sin60
Then redo the hypotenuse.
THE SIDES ON A 30-60-90 TRIANGLE:
Short Side = x
Long Side = sqrt(3)*x
Hypotenuse = 2x
In this case:
Short Side = 7.5
Long Side = sqrt(3)*7.5
Hypotenuse = 2*7.5
Oops :O
Thanks
Thanks :)
To determine if you have done this correctly, let's go through the steps together:
In a 30°-60°-90° right triangle, the relationship between the side lengths can be determined by the ratios of the sides.
The ratios for this triangle are:
Short leg : Long leg : Hypotenuse = 1: √3: 2
Given that the shorter leg is 7.5 inches, we can use these ratios to find the lengths of the longer leg and the hypotenuse.
To find the longer leg, we need to use the ratio:
7.5 / sin(60°) = b / sin(30°)
To solve for b, multiply both sides of the equation by sin(30°):
7.5 * sin(30°) / sin(60°) = b
Plugging in the values:
b = 7.5 * (1/2) / (√3/2)
b = 7.5 / √3
b ≈ 4.33 inches
So, the longer leg is approximately 4.33 inches.
To find the hypotenuse, we can use the ratio:
7.5 / sin(30°) = c / sin(90°)
Since sin(90°) = 1, the equation becomes:
7.5 = c / 1
So, the hypotenuse is 7.5 inches.
Based on these calculations, it appears that you have made a mistake in your calculations for the longer leg. Instead of 4.208723391 inches, the correct answer is approximately 4.33 inches. However, your calculation for the hypotenuse of 8.6 inches is correct.