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?

Solving Right Triangles Geometry

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

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

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.

Given One Side Length and one acute angle 18 y 62° B x A

Given Two Side Lengths C 8 B 6 A

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

Given Two Side Lengths C 8 B 6 A

Solve the Right Triangle

Solve the Right Triangle

Solve the Right Triangle

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

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.