Section 9-3 Angles of Elevation and Depression SPI 32F: determine the trigonometric ratio for a right triangle needed to solve a real-world problem given a diagram Objectives: Use angles of Elevation and Depression to solve problems Sin  = opposite leg hypotenuse Cos  = adjacent leg hypotenuse Tan  = opposite adjacent Tan -1 = opposite adjacent Sin -1 = opposite hypotenuse Cos -1 = adjacent hypotenuse Use if you have an angle measure Use if you need to find angle measures

Angles of Elevation and Depression Angle of Elevation: Person on the ground looks at an object Angle of Depression Person looks down at an object Why are the two angles congruent? Transversal and parallel lines (alternate interior angles)

Describe  1 and  2 as they relate to the situation shown. 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. 2 is the angle of elevation from the building to the airplane. Angles of Elevation and Depression

A theodolite is an instrument for measuring both horizontal and vertical angles, as used in triangulation networks. It is a key tool in surveying and engineering work, but theodolites have been adapted for other specialized purposes in fields like metrology and rocket launch technology. angles triangulation surveying engineeringmetrologyrocket launch technology Theodolite

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. x = 200 tan 35° Solve for x. Use the tangent ratio.tan 35° = x 200 Use a calculator So x 140. To find the height of the building, add the height of the Theodolite, which is 5 ft tall. The building is about 140 ft + 5 ft, or 145 ft tall. Angles of Elevation and Depression

An airplane flying 3500 ft 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. Use the sine ratio.sin 2° = 3500 x x = 3500 sin 2° Solve for x Use a calculator Divide by 5280 to convert feet to miles. The airplane is about 19 mi from the airport when it starts its descent. Angles of Elevation and Depression