A 45-45-90 triangle has a hypotenuse with a length of 10 feet.
What are the lengths of the other legs?
9.14 ft.
6.36 ft.
8.46 ft.
7.07 ft.
To find the lengths of the legs of a 45-45-90 triangle, you can use the ratios between the sides. In a 45-45-90 triangle, the two legs are congruent, meaning they have equal lengths.
The ratio between the lengths of the legs and the hypotenuse in a 45-45-90 triangle is 1:1:√2.
Given that the hypotenuse has a length of 10 feet, we can calculate the lengths of the legs.
Length of each leg= (Length of hypotenuse)/√2
Length of each leg= 10 ft/√2
To simplify the denominator, multiply the fraction by (√2)/(√2):
Length of each leg= (10 ft/√2) * (√2)/(√2)
Simplifying, we get:
Length of each leg= 10√2/2
Length of each leg= 5√2
Using a calculator to approximate the value of √2 as 1.414, we get:
Length of each leg= 5 * 1.414
Length of each leg= 7.07 ft
Therefore, the lengths of the legs of the 45-45-90 triangle are approximately 7.07 ft each.
To find the lengths of the other legs of a 45-45-90 triangle, we can use the ratios of the sides. In a 45-45-90 triangle, the two legs are congruent, meaning they have the same length, and the hypotenuse is the length of the legs times the square root of 2.
Let's label one of the legs as "x" and the hypotenuse as "10 feet." According to the ratio, x * (square root of 2) = 10 feet.
To solve for x, divide both sides of the equation by the square root of 2:
x = 10 feet / (square root of 2)
To simplify this, multiply both the numerator and denominator by the conjugate of the denominator, which is also the square root of 2:
x = (10 feet / (square root of 2)) * ((square root of 2) / (square root of 2))
This simplifies to:
x = (10 feet * (square root of 2)) / 2
x = 5 feet * (square root of 2)
Calculating the value, 5 feet * (square root of 2) is approximately 7.07 feet. Therefore, the length of each leg in the 45-45-90 triangle is 7.07 feet.
Try Pythagorean theorem.
x^2 + x^2 = 10^2
Solve for x.