Warm-Up: For the right triangle ABC shown below, find the values of b and c. Hint: Hint: Think about the side you know, the side you want to find out, and which trigonometric ratio compares the two. b = c = 85.20

13.1 – Solving Right Triangles (Inverses and Angles of Elevation/Depression)

Example 1: For the right triangle ABC shown, find the value of b and, and. Solving for Angle Measures Using Inverse Trigonometry Use inverse trigonometry to find out angle measures! b = 12 A = B = 67.38

Example 2: For the right triangle ABC shown, find the values of a and b. Hint: Hint: Think about the side you know, the side you want to find out, and which trigonometric ratio compares the two. * Use inverses to find the third side! * a = b = A = 16

Example 3: Find the measure of angle Ө. Ө = Ө = Ө = 35.69

Describe 1 and 2 as they relate to the situation shown. angle of depression One side of the angle of depression is a horizontal line. 1 is the angle of depression from the airplane to the building. One side of the angle of elevation is a horizontal line. angle of elevation 2 is the angle of elevation from the building to the airplane.

A surveyor stands 200 ft from a building to measure its height with a 5-ft tall theodolite. The angle of elevation to the top of the building is 35°. How tall is the building? Draw a diagram to represent the situation. To find the height of the building, add the height of the theodolite, which is 5 ft tall ft

An airplane flying 3500 feet above ground begins a 2° descent to land at an airport. How many miles from the airport is the airplane when it starts its descent? Draw a diagram to represent the situation ft

Example 4: The highest tower in the world is in Toronto, Canada, and is 553 m high. An observer at point A, 100 m from the center of the tower’s base, sights the top of the tower. The angle of elevation is  A. Find the measure of this angle to the nearest hundredth of a degree °

Homework: pg. 773 #43-46 and pg. 795 #26-31