The shorter leg of a 30°–60°–90° triangle is 10.

What are the lengths of the longer leg and the
hypotenuse, to the nearest tenth?

Explain how to find the lengths of the longer leg and hypotenuse of a 30°-60°-90° triangle if the shorter leg is 10 ft.

a right triangle has a leg measuring 52 meters and a hypotenuse measuring 63 meters. what is the measurement of the other leg?

Well, we have a 30°–60°–90° triangle and you mentioned that the shorter leg is 10. Let's call the shorter leg "x".

According to the ratios for a 30°–60°–90° triangle, the longer leg is always equal to x√3 and the hypotenuse is always 2x.

Therefore, in this case, the longer leg would be 10√3 (approximately 17.320508) and the hypotenuse would be 2 * 10 = 20.

So, to the nearest tenth, the length of the longer leg would be approximately 17.3 and the length of the hypotenuse would be 20.

To find the lengths of the longer leg and the hypotenuse of a 30°–60°–90° triangle, we can use the ratios of the side lengths in this special triangle.

In a 30°–60°–90° triangle, the side opposite the 30° angle is the shorter leg, the side opposite the 60° angle is the longer leg, and the side opposite the 90° angle is the hypotenuse.

The ratios of the side lengths in a 30°–60°–90° triangle are as follows:

Shorter leg : Longer leg : Hypotenuse = 1 : √3 : 2

Given that the shorter leg is 10, we can use this ratio to find the lengths of the longer leg and the hypotenuse.

Using these ratios, we can calculate:

Longer leg = Shorter leg × √3 = 10 × √3 ≈ 17.3 (rounded to the nearest tenth)

Hypotenuse = Shorter leg × 2 = 10 × 2 = 20

Therefore, the lengths of the longer leg and the hypotenuse of the 30°–60°–90° triangle, to the nearest tenth, are approximately 17.3 and 20, respectively.

The shorter leg of a 30°–60°–90° triangle is 10.

What are the lengths of the longer leg and the
hypotenuse, to the nearest tenth?
can you help me to understand?
I know that
The length of the hypotenuse of any 30°–60°–90° triangle is two times the length of
the shorter leg. The length of the longer leg is the length of the shorter leg times square root of 3. ?

10 ft being the long leg x being the short leg and y being the hypotenuse