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A day full of math games & activities. Find one near you.
In a 30-60-90 triangle, what is the length of the hypotenuse when the shorter leg is 8 m?
Solution:
Given, the length of the shorter leg is 8m.
Let the side opposite to 30° be the shortest leg.
The side opposite to 60° is the longest leg.
So, the side opposite to 90° is hypotenuse.
Length of the shortest side is x.
Length of longest side is √3(x)
Length of the hypotenuse is 2x.
We know, x = 8
So, √3(x) = √3(8)
Thus, the length of the longer leg is √3(8) m.
Length of hypotenuse = 2x = 2(8) = 16m
We can also use Pythagoras theorem,
x2 + (√3 x)2 = (2x)2
(8)2 + (√3(8))2 = (2x)2
64 + (3(64)) = (2x)2
(2x)2 = 64 + 192
(2x)2 = 256
Taking square root on both sides,
2x = √256
2x = 16
Therefore, the length of the hypotenuse is 16m.
In a 30-60-90 triangle, what is the length of the hypotenuse when the shorter leg is 8 m?
Summary:
In a 30°-60°-90° triangle, the length of the shorter leg is 8m. The length of the hypotenuse is 16m.