Practice Problems 1. In a 30-60-90 triangle , what is the length of the hypotenuse when the shorter leg is 8m?

1.

In all 30-60-90 triangles:

the shortest side—across from the 30º angle = n

the middle length side—across from the 60º angle = √(3)n

the longest side/hypotenuse—across from the 90º angle = 2n

So..... if the shortest side = n = 8

The hypotenuse = 2n = 2(8) = 16 meters

2.

In all 45-45-90 triangles:

both legs—across from the 45º angles = n

the hypotenuse—across from the 90º angle = √(2)n

So...if a leg = n = 5

The hypotenuse = √(2)n = √(2)(5) = 5√(2) ≈ 7.071 inches

3.

x is one of the legs of a 45-45-90 triangle.

The other leg is the hypotenuse of a 30-60-90 triangle.

Both legs are the same length in a 45-45-90 triangle.

So..

Find the hypotenuse of the 30-60-90 triangle when the middle length side = 2√(3)

and that will be the same length as x.

Can finish this one on your own? It is now very similar to problem number 1.

4.

The sin(45º) = the length of a leg in a 45-45-90 triangle when the hypotenuse is 1.

So..

Find the length of a leg in a 45-45-90 triangle when the hypotenuse = 1

and that will be sin(45º)

Can you finish it on your own? It is very similar to problem number 2.

5.

Here is an illustration:

area of hexagon = 12 * area of third triangle.

area of third triangle = (1/2) * base * height

area of third triangle = (1/2) * 6 * orange line

area of third triangle = 3 * orange line

area of third triangle = 3 * √(3)(6)

area of third triangle = 18√3

area of hexagon = 12 * 18√3

area of hexagon = 216√3 ≈ 374.123 sq. cm.

Thanks!