Solving Right Triangle Application

We have learned about the ratios for the six trig functions, so what can we do with these? Well we can use them to find missing angles and sides for any right triangle.

As long as we know 2 of the parts to the trig ratio we can find the third part.For example if we know an acute angle and the opposite side we could use sine or cosecant to find the hypotenuse and we could use tangent or cotangent to find the adjacent side.

Building

In real life problems the angles are not called A,B and, C but instead we use the terms angle of elevation or depression.

Angles of elevation or depression are made with a horizontal line.

Angle of elevation

Angle of depression

To find this angle – the angle of depression from 90

Once you fill in the angles you can use trig ratios to find the sides.

Washington monument

A surveyor is standing 115 feet from the base of the Washington Monument. The surveyor measures the angle of elevation to the top of the monument as 78.30. To the nearest foot, how tall is the Washington Monument?

Angle of elevation78.30

115 feet

What trig ration can we use to find the height of the monument?x

Building

The angle of depression from the top of a building to a point on the ground is 46.50. To the nearest tenth, how far is the point on the ground to the top of the building if the building is 78 m high?

What trig ration can we use to find the height of the monument?

x78

Angle of depression

To find this angle – the angle of depression from 9090 – 46.5 = 43.50