A 30°–60°–90° triangle has a hypotenuse with a length of 18.
What is the length of the shorter leg of the triangle?
sides of a 30-60-90 triangle are in the ratio of
1 : √3 : 2
so x : ? : 18 = 1 : √3 : 2
x/1 = 18/2
x = 9
The shorter leg of 30-60-90 degree triangle is 6. What is the hypotenuse?
To find the length of the shorter leg of a 30°-60°-90° triangle, we can use the ratio of the side lengths.
In a 30°-60°-90° triangle, the ratio of the sides is:
Shorter leg : Hypotenuse : Longer leg
1 : √3 : 2
Given that the hypotenuse has a length of 18, we can set up the following equation using the ratio:
x : 18 : √3x = 1 : √3 : 2
To solve for x, we can cross-multiply:
18 * √3 = x * 2
Simplifying,
√3 = 2x/18
Dividing both sides by 2,
√3/2 = x/18
To isolate x, we can multiply both sides by 18,
x = (18 * √3)/2
Simplifying further,
x = 9√3
Therefore, the length of the shorter leg of the triangle is 9√3.