Transcript 9-3 PPT Angles of Elevation and Depression

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
Use if you have an angle measure
Use if you need to find angle measures
Tan  = opposite
adjacent
Tan -1 = opposite
adjacent
Sin  = opposite leg
hypotenuse
Sin -1 = opposite
hypotenuse
Cos = adjacent leg
hypotenuse
Cos -1 = adjacent
hypotenuse
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)
Angles of Elevation and Depression
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.
Theodolite
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 of Elevation and Depression
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
tan 35° = 200
Use the tangent ratio.
x = 200 • tan 35°
200
35
140.041508
So x
Solve for x.
Use a calculator.
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.
sin 2° =
x=
3500
2
5280
100287.9792
18.993935
3500
x
3500
sin 2°
Use the sine ratio.
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.