Solving Trig Problems Precal – Section 4.8

Angle of Elevation and Depression The angle of elevation is measured from the horizontal up to the object. Imagine you are standing here.

Angle of Elevation and Depression The angle of depression is measured from the horizontal down to the object. Constructing a right triangle, we are able to use trig to solve the triangle. A second similar triangle may also be formed.

Angle of Elevation and Depression Example #1

Angle of Elevation and Depression Suppose the angle of depression from a lighthouse to a sailboat is 5.7 o. If the lighthouse is 150 ft tall, how far away is the sailboat? Construct a triangle and label the known parts. Use a variable for the unknown value. 5.7 o 150 ft. x

Angle of Elevation and Depression Suppose the angle of depression from a lighthouse to a sailboat is 5.7 o. If the lighthouse is 150 ft tall, how far away is the sailboat? 5.7 o 150 ft. x Set up an equation and solve.

Angle of Elevation and Depression 5.7 o 150 ft. x Remember to use degree mode! x is approximately 1,503 ft.

Angle of Elevation and Depression Example #2

Angle of Elevation and Depression A spire sits on top of the top floor of a building. From a point 500 ft. from the base of a building, the angle of elevation to the top floor of the building is 35 o. The angle of elevation to the top of the spire is 38 o. How tall is the spire? Construct the required triangles and label. 500 ft. 38 o 35 o

Angle of Elevation and Depression Write an equation and solve. Total height (t) = building height (b) + spire height (s) 500 ft. 38 o 35 o Solve for the spire height. t b s Total Height

Angle of Elevation and Depression Write an equation and solve. 500 ft. 38 o 35 o Building Height t b s

Angle of Elevation and Depression Write an equation and solve. 500 ft. 38 o 35 o The height of the spire is approximately 41 feet. t b s Total height (t) = building height (b) + spire height (s)

Angle of Elevation and Depression Example #3

Angle of Elevation and Depression A hiker measures the angle of elevation to a mountain peak in the distance at 28 o. Moving 1,500 ft closer on a level surface, the angle of elevation is measured to be 29 o. How much higher is the mountain peak than the hiker? Construct a diagram and label. 1 st measurement 28 o. 2 nd measurement 1,500 ft closer is 29 o.

Angle of Elevation and Depression Adding labels to the diagram, we need to find h. 28 o 29 o 1500 ftx ft h ft Write an equation for each triangle. Remember, we can only solve right triangles. The base of the triangle with an angle of 28 o is x.

Angle of Elevation and Depression Now we have two equations with two variables. Solve by substitution. Solve each equation for h. Substitute.

Angle of Elevation and Depression Solve for x. Distribute. Get the x’s on one side and factor out the x. Divide. x = 35,291 ft.

Angle of Elevation and Depression However, we were to find the height of the mountain. Use one of the equations solved for “h” to solve for the height. x = 35,291 ft. The height of the mountain above the hiker is 19,562 ft.

Angle of Elevation and Depression Start homework on a new page. Assignment 4.8 / 1, 3, 8, 11, 14-16, 19, 26 Quiz Friday Homework up to today is due Friday. Remember to change your calculator between radians and degrees when required. All graphing of trig functions is done in radians.