Unit 4 - Objective 5 - Application of Right Triangles


Sometimes when solving problems involving trigonometry, we have to use the angle of elevation, which is the angle measured from the horizontal through which an observer would have to elevate his or her line of sight in order to see the object.

elevate.gif (2858 bytes)

The angle of depression is the angle measured from the horizontal, through which an observer has to lower his or her line of sight in order to see an object.

depress.gif (2926 bytes)

Examples:

1. A person is standing 50m from the base of a tower.  The angle of elevation to the top of the tower is 76 degrees.  How high is the tower?
tower.jpg (20321 bytes)

Solution - The Height of the tower is x. So we have:

tan 76 = x / 50
50 tan 76 = x
50 (4.0107809) = x
200.5m approx_g.gif (145 bytes) x

2. Two people are in a hot air balloon.  One of them is able to get a sighting as it passes over one end of a football field.  The angle of depression to the other end of the football field is 53.8 degrees.  This person knows that the length of the football field, including the end zones is 120 yards.  How high was the balloon when it went over the football field?
football.jpg (32539 bytes)

Solution - The Height has been labled h.  We have:

tan 53.8 = h / 120
120 tan 53.8 = h
120 (1.366326733) = h
164yd approx_g.gif (145 bytes) h

 


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