The length of the longer leg of a 30-60-90 triangle is 24 feet. How do I find the length of the hypotenuse of the triangle? The answer must be a radical in simplest form.
A 30-60-90 triangle has sides in the ratio:
1 : √3 : 2
Find the remaining sides by proportion.
To find the length of the hypotenuse of a 30-60-90 triangle when you know the length of one leg, you can use the following relationship:
Hypotenuse = 2 * (longer leg)
In this case, the length of the longer leg is given as 24 feet. So, substituting the value into the formula, we get:
Hypotenuse = 2 * 24
Simplifying further:
Hypotenuse = 48 feet
Therefore, the length of the hypotenuse of the triangle is 48 feet.
To find the length of the hypotenuse in a 30-60-90 triangle, we can use the relationship between the sides. In a 30-60-90 triangle, the longer leg is always equal to the shorter leg times the square root of 3. So, if the length of the longer leg is given as 24 feet, we can find the length of the shorter leg by dividing 24 by the square root of 3.
Finding the square root of 3 involves the use of a calculator or a mathematical software. In this case, the square root of 3 is approximately 1.732.
So, the length of the shorter leg can be calculated as:
Shorter leg = 24 / √3 ≈ 24 / 1.732 ≈ 13.856 feet
Now, to find the length of the hypotenuse, we can use the relationship that the hypotenuse is always equal to twice the length of the shorter leg. Multiplying the length of the shorter leg by 2 gives us:
Hypotenuse = 2 * 13.856 ≈ 27.712 feet
Therefore, the length of the hypotenuse of the 30-60-90 triangle is approximately 27.712 feet.