Question

The length of the hypotenuse of 30 -60 -90 triangle is 4 find the longer leg

Answer 1

the longer leg is the leg adjacent to the larger angle

so 60

length of longer leg = 4 sin60 = 2sqrt(3)

Answer 2

`2√(3)` units is the longer leg

Explanation:

Definition: 30 -60 -90

In 30-60-90 triangle,

the length of the hypotenuse is twice the length of the shorter leg; and

the length of the longer leg is
`√(3)` times the length of the shorter leg.

As per the statement:

The length of the hypotenuse of 30 -60 -90 triangle is 4

Length of hypotenuse = 4 units

then, by definition we have;

length of shorter leg = 2 units

then;

the length of the longer leg is
`√(3)` times the length of the shorter leg.

⇒Length of longer leg =
`2√(3)` units

Therefore, the length of longer leg is,
`2√(3)` units