Angle of Elevation & Depression

Angle of Elevation & Depression

I can solve for a missing side length or angle using a sine, cosine, or tangent ratio.

Multiple Choice

Does this picture represent an angle of elevation or depression?

• Elevation

• Depression

Multiple Choice

Does this picture represent an angle of elevation or depression?

• Elevation

• Depression

Multiple Choice

Does this picture represent an angle of elevation or depression?

• Elevation

• Depression

Multiple Choice

Does this picture represent an angle of elevation or depression?

• Elevation

• Depression

Multiple Choice

Does this picture represent an angle of elevation or depression?

• Elevation

• Depression

Example 1:

Suppose you are a lifeguard looking down at a swimmer in a swimming pool. Your line of sight forms a 55 degree angle of depression. You are 10 ft up in your lifeguard seat.

How far is the swimmer from the base of your lifeguard stand?

Step 1: draw your picture based on the problem

Suppose you are a lifeguard looking down at a swimmer in a swimming pool. Your line of sight forms a 55 degree angle of depression. You are 10 ft up in your seat.

How far is the swimmer from the base of your lifeguard stand?

Step 2: Label your picture based on problem

Suppose you are a lifeguard looking down at a swimmer in a swimming pool. Your line of sight forms a 55 degree angle of depression. You are 10 ft up in your seat.

How far is the swimmer from the base of your lifeguard stand?

Label your angle inside of triangle

They are alternate interior angle so they are congruent (same)

Multiple Choice

Step 3: Label your sides of the triangles

What side is the 10?

• opposite

• adjacent

• hypotenuse

Multiple Choice

What side is the x?

• opposite

• adjacent

• hypotenuse

Multiple Choice

Which trig ratio are you going to use to solve this problem?

hint: SOH CAH TOA

• Sin

• Cos

• Tan

Multiple Choice

Step 4: Set up your equation

What equation would be used to solve this problem?

• $\tan x=\frac{10}{55}$

• $\tan55=\frac{10}{x}$

• $\tan55=\frac{x}{10}$

• $\sin55=\frac{10}{x}$

Step 5: Cross multiply and solve using calculator

Use desmos as calculator

Multiple Choice

A salvage ship uses sonar to determine that the angle of depression to a wreck on the ocean floor is 13 degrees. The depth chart shows that the ocean floor is 40 meters below the surface. What equation would be used to find how far the diver must walk along the ocean floor to reach the wreck?

•  $\tan x=\frac{13}{40}$  

•  $\tan13=\frac{40}{x}$  

•  $\tan13=\frac{x}{40}$  

•  $\cos x=\frac{13}{40}$  

Multiple Choice

A sledding run is 300 yards long with a vertical drop of 27.6yds. What equation would be used to find the angle of depression of the run?

• $\tan x=\frac{27.6}{300}$
  

• $\cos x=\frac{27.6}{300}$

• $\cos x=\frac{300}{27.6}$

• $\sin x=\frac{27.6}{300}$

Multiple Choice

Little Suzie let go of her balloon. It floated to the to of the gym, 50ft above the ground. Her big brother is standing 60ft away. What equation would you use to find the angle of elevation from him to the balloon?

• $\tan x=\frac{50}{60}$

• $\tan x=\frac{60}{50}$

• $\sin x=\frac{60}{50}$

• $\cos x=\frac{50}{60}$