The length of the longer leg of a 30°– 60°– 90° triangle with hypotenuse length 4 is _____
I do not understand how to figure this out.
To figure out the length of the longer leg of a 30°– 60°– 90° triangle with a given hypotenuse length, you can use the ratios of the side lengths in this special triangle.
In a 30°– 60°– 90° triangle, the ratio of the side lengths is 1:√3:2. This means that the shorter leg is half the length of the hypotenuse, and the longer leg is √3 times the length of the shorter leg.
Since the hypotenuse in this case has a length of 4, the shorter leg would be half of that, which is 2 (4/2 = 2).
Now, to find the length of the longer leg, you can multiply the length of the shorter leg by √3:
Length of longer leg = (√3)(2) = 2√3
Therefore, the length of the longer leg of the 30°– 60°– 90° triangle with a hypotenuse length of 4 is 2√3.
The sides of the 30°-60°-90° are in the ratio of
1 : √3 : 2
so yours is a : b : 4
b/√3 = 4/2
b = 2√3