Angles of Elevation and Depression
Standard
G.SRT.8 Use trigonometric ratios to solve right triangles in applied problems.
Goals for this section:
Students will learn what an angle of elevation and an angle of depression are.
Object A is on the ground while Object B is up in the air. The line that connects them is the distance between A and B.
They form an angle of elevation and an angle of depression. They're congruent since they're alternate interior angles.
Examples:
1. An airplane pilot sights a boat at a 29 degree angle of depression. The airplane's altitude is 3.5 km. What is the airplane's horizontal distance from the boat?
Create a picture. What does altitude mean?
Here's the picture, but do try drawing it yourself first!
To find the horizontal distance SOH CAH TOA will be used, which we will go more in depth in Unit 6. SOH CAH TOA stands for trigonometric functions and their ratios in a right triangle.
- SOH stands for Sin(Θ) = Opposite / Hypotenuse
- CAH stands for Cos(Θ) = Adjacent / Hypotenuse
- TOA stands for Tan(Θ) = Opposite / Adjacent
- Θ (greek letter theta) is the angle that we are using in the triangle besides the 90 degree angle.
The triangle will need to be labeled in order to figure out which ratio we will use. Do we have the measurements for opposite, adjacent, or hypotenuse? What's Θ? This will help us find the horizontal distance.