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 hypotenuseCos = 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 anobject
Angle of Depression Person looks down at anobject
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.
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.200 35 140.041508
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.
3500 2 100287.9792 Use a calculator.
5280 18.993935 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
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