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.

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.

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?

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 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?

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

 tan 53.8° = h / 120 120 tan 53.8° = h 120 (1.366326733) = h 164yd h

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