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

2. In a 45-45-90 triangle, what is the length of the hypotenuse when the length of one of the legs is 5in?

3. What is the value of x?

4. What is the exact value of sin 45dg? Answer as a simplified fraction.

5. What is the area of a regular hexagon with a side length of 12cm? Round final answer to the nearest hundredth.

KenyaRT
Apr 9, 2017

#1**+3 **

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.

hectictar
Apr 9, 2017

#1**+3 **

Best Answer

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.

hectictar
Apr 9, 2017