1. Example
A certain part of a hiking trail slopes upward at about a 5° angle. After traveling a horizontal distance of 100 feet along this part of the trail, what would be the change in a hiker’s vertical position? What distance has the hiker traveled along the path?

2. Solving Right Triangles
Geometry

3. RIGHT TRIANGLE
Parts
1 right angle
2 acute angles
1 hypotenuse
2 legs

4. SOLVE A RIGHT TRIANGLE
To solve a right triangle means to find the measures of all three angles and all three sides.

5. In order to solve a right triangle…
You can solve a right triangle if you know either of the following
Two side lengths
One side length and one acute angle measure.

6. Given One Side Length and one acute angle18 y
62° B x A

7. Given Two Side Lengths C 8 B 6 A

8. Finding the angles
Once you know the sine, the cosine, or the tangent of an acute angle, you can use a calculator to find the measure of the angle. If sin A = x, then sin-1 x = A If cos A = y, then cos-1 y = A If tan A = z, then tan-1 z = A

9. Given Two Side Lengths C 8 B 6 A

10. Solve the Right Triangle

11. Solve the Right Triangle

12. Solve the Right Triangle

13. Solving a Right Triangle
Given two sides
Given 1 side and 1 acute angle
Find the third side by Pythagorean Theorem
Set up a trig function for an acute angle
Use the inverse of that trig function to find the measure of the angle
Then repeat for the other angle or use the triangle sum theorem
Use triangle sum theorem to find the other angle
Use trig functions to find the other two lengths

14. How do I know when to use the inverse button?
Use the inverse button when we have the ratio set up and we are trying to find the angle.