A 30°–60°–90° triangle has a hypotenuse with a length of 18.
What is the length of the shorter leg of the triangle?
A.5
B.5 sqrt 3
C.5 sqrt 2
D.20
Don't understand.
I think it is 5sqrt 3
sin 30 = 1/2
so
1/2 = short side/hypotenuse = short side/18
so
short side = 9
which is none of the above.
To find the length of the shorter leg of the 30°–60°–90° triangle, we need to know the relationships between the sides of this special triangle. In a 30°–60°–90° triangle, the sides are proportional to each other.
The ratios between the sides in a 30°–60°–90° triangle are:
Shorter leg: longer leg = 1 : √3
Hypotenuse: shorter leg = 2 : 1
Hypotenuse: longer leg = 2 : √3
Since the hypotenuse in this triangle has a length of 18, we can find the length of the shorter leg using the second ratio:
Hypotenuse: shorter leg = 2 : 1
Let's set this up as a proportion:
18 : x = 2 : 1
This can be written as:
18 / x = 2 / 1
To solve for x, we can cross-multiply:
18 * 1 = 2 * x
18 = 2x
Dividing both sides by 2, we get:
x = 9
So the length of the shorter leg of the 30°–60°–90° triangle is 9.
Therefore, the correct answer is not listed among the options provided.