Using Sine in Real Life

I created this triangle to use sine, cosine, or tangent to figure out a missing length. When I measured the angles it turned out that this triangle was a 30, 60, 90 triangle. The shelf leg forms an approximate 90 degree angle with the ground. Angle G is 60 degrees, and Angle E is 30 degrees.

Given: Angle of Depression = 60 degrees

            From the figure to the base of the shelf is 60 cm

Find: Height of shelf (AB)

By using the given information we can figure out a lot of things.

1. Angle C = 60 degrees

2. AC = 120 cm by using 30, 60, 90 triangle rules

We could find AB by using the 30-60-90 way, but let's use sine. Let's say AB, the height of the shelf, is x.

Sine=opposite/hypotenuse

sin(60 degrees) = x/120

120*sin(60) = x

x is approximately 104cm

If you check using the 30, 60, 90 way this is how it would be:

BC= 60

AB= 60√(3)

AB= 102

102 is approximately 104, check!

~SV1