Solving Word Problems Using TrigonometryMs. BakerTaylor Road MSMarch, 2013

New Vocabulary

Several new terms are used in word problems, and you need to know them!

Angle of DepressionAngle of Depression In the diagram at the

left, x marks the angle of depression of a boat at sea from the top of a

lighthouse.You can think of the

angle of depression in relation to the

movement of your eyes. You are standing

at the top of the lighthouse and you are looking straight ahead.

You must lower (depress) your eyes to

see the boat in the water.

Angle of ElevationAngle of Elevation The angle of elevation is

always measured from the ground up. Think of it like an elevator that only goes up. In the diagram at the left, x marks the angle of elevation of the top of the tree as seen from a point

on the ground.You can think of the angle of elevation in relation to

the movement of your eyes. You are looking

straight ahead and you must raise (elevate) your eyes to see the top of the

tree.

A little more information…

As seen in the diagram above of angle of depression, the dark black horizontal line is parallel to side CA of triangle ABC. This forms alternate interior angles which are equal in measure (so, x also equals the measure of ).

Simply stated, this means that:the angle of elevation = the angle of depression.

BAC

More about Angles of DepressionThere are two possible ways to use our angle of depression to obtain an angle INSIDE the triangle.1. Find the angle adjacent to

our angle which is inside the triangle. This adjacent angle will always be the complement of our angle. In other words, the angles will add to 90º. In the diagram on the left, the adjacent angle is 55º.

2. Utilize the fact that the angle of depression = the angle of elevation and simply place 35º in angle A. (the easiest method) Just be sure to place it in the proper position.

Subtended Angle

This is an angle formed by an external point.

It’s easier to see, than describe…so click on the link to see a great example!

http://www.mathopenref.com/subtend.html

Your turn…1. A ramp is to be placed from a loading platform onto the back of a truck. The truck can get no closer than 3 feet to the platform. The truck bed is 1.5 feet higher than the loading platform. Find the angle of elevation from the platform to the truck bed.

Make a drawing!!truck bed

loading platform3 feet

1.5 feet

Now…Solve

3

5.1tan

)5(.tan 1

6.26

One more for good luck!

2. A jet is flying at an altitude of 30,000 feet. An air traffic controller measures the angle of elevation to the plane to be 16.5°. Find the horizontal distance of the plane from the airport.

Draw a picture! – It really helps, I promise.

airplane

air traffic controller

30000 feet

d = Distance from airport

d

16.5°

Solve!

So…The airplane is 101278.3 feet from the airport.

3.1012785.16tan

30000

30000)5.16(tan

300005.16tan

d

d

dd