4B Examples Angle of Elevate and Depress.ppt

Mathematics

1. Angles of Elevation & Angles of Depression
The angle of elevation is the angle between a horizontal line from
the observer and the line of sight to an object that is ABOVE the
horizontal line.

2. The angle of depression is the angle between a horizontal line
from the observer and the line of sight to an object that is BELOW
the horizontal line.

3. Solving word problems involving angles of elevation & depression.
1) Read the problem and visualize what it looks like. Then draw a
sketch and label the known values (side lengths, angles, etc.). The
triangle should be drawn to scale. It is normally a right triangle.
2) Use trig functions (sin, cos, or tan) and the Pythagorean theorem
(a
2
+ b
2
= c
2
) to find the length of missing sides (sin θ, cos θ, tanθ) or
angles (sin
-1
, cos
-1
, tan
-1
).
3) Solve for the missing part. Put units on the answer. Sides of the
triangle are lengths (feet, km, etc.) and angles are measured in
degrees.

4. John wants to measure the height of a tree. He walks exactly
100 feet from the base of the tree and looks up. The angle
from the ground to the top of the tree is 33º . How tall is the
tree?

5. A building is 50 feet high. At a distance away from the
building, an observer notices that the angle of elevation to
the top of the building is 41º. How far is the observer from the
base of the building?

6. An airplane is flying at a height of 2 miles above the ground.
The distance along the ground from the airplane to the
airport is 5 miles. What is the angle of depression from the
airplane to the airport?

7. A bird sits on top of a lamppost. The angle of depression from
the bird to the feet of an observer standing away from the
lamppost is 20 degrees. The distance from the bird to the
observer is 25 meters. How tall is the lamppost?

8. A tight-rope walker is going to walk between two buildings.
One building is 100 feet high. The other building is 140 feet
high. If the angle of elevation from the top of the shorter
building to the top of the taller building is 8 degrees, how
long of a wire would it take to reach from the edge of one
building's roof to the other's?