21+Angle+of+Elevation+and+Depression

**Angle of Elevation and Depression:**
__Elevation__ - the angle that an observer would raise his or her line of sight above a horizontal line in order to see an object. __Depression__ - if an observer were up above and needed to look down, the angle of depression would be the angle that the person would need to lower his or her line of sight.
 * GOAL:** Solve for the angle of depression/elevation or a side length in a problem using trigonometry (SOH CAH TOA - sine, cosine, tangent)

In order to solve problems involving angles of elevation and depression, it is necessary to > A typical problem of angles of elevation and depression involves organizing information regarding distances and angles within a right triangle. In some cases, you will be asked to determine the measurement of an angle; in others, the problem might be to find an unknown distance. Suppose a tree 50 feet in height casts a shadow of length 60 feet. What is the angle of elevation from the end of the shadow to the top of the tree with respect to the ground? First we should make a diagram to organize our information. Look for these diagrams to involve a right triangle. In this case, the tree makes a angle 90º with the ground. A diagram of this right triangle is shown below. In the diagram, known distances are labeled. These are the 50 and 60 foot legs of the right triangle corresponding to the height of the tree and the length of the shadow. The variable q is chosen to represent the unknown measurement, the object of the question. To relate the known distances and the variable, an equation is written. In this case the equation involves the lengths of the sides which are opposite and adjacent to the angle q. Using the ratio of opposite to adjacent sides, we have.
 * use basic right triangle trigonometry
 * solve equations which involve one fractional term is also important to know.
 * find an angle given a right triangle ration of sides.
 * the fact that corresponding angles formed by parallel lines have the same measure.

__Examples__ 1. A duck, flying 10 miles above the ground, is 4 miles away from a lake. The angle of depression from the duck to the lake is 25°. What is the distance that the duck needs in order to descend from the air to the lake?

2. At a point on the ground 40 feet from the foot of a tree, the angle of elevation of the top of the tree is 42°. Find the height of the tree to the nearest tenth.

3. A burning building is 10 feet above the ground and is 5 feet away from a fire truck. The angle of depression from the building's flames to the fire truck is 30°. How far must the water jet pumped from the fire truck’s hose reach in order to extinguish the flames?

__Answers__ 1. sin25°=10/x x(sin25)=10 x= 10/sin25 x=23.7 miles

2. tan42=x/40 40(tan42)=x x=36 feet

3. cos30=10/x x(cos30)=10 x=10/cos30 x=11.5 feet

Websites: [|Angle of Depression] [|Angle of Elevation] [|Angle of Elevation/Depression]