Applications AWS
September 23, 2016
Inverse Functions
Inverse Functions and
Applications
Algebraically:
or
Verbally: they both mean - find the angle whose sin is Numerically: The answer.
Numerical 1)
2)
September 23, 2016
3)
4)
5) Find the value of 5
6) Find the value of
7
9 4
September 23, 2016
7) Find the value of
8) Find the value of 50 16 33
Find the value of x. All angles given in degrees.
10)
9) x
25 43
10
x 37
Solve the triangle. 11) x
17
40
September 23, 2016
Find the missing side -
Find the missing side -
80
9
x
x
APPLICATION
Using the Inverse Function
A competitor in a triathlon is running along the course shown. Determine the length in feet that the runner must cover to reach the finish line. Runner
200 ft
Finish Line
September 23, 2016
Suppose a competitor in the swimming portion of the race is swimming along the course shown. Find the distance the competitor must swim to reach the shore.
Swimmer
Finish Line
Angle of depression and angle of elevation
Angle of Depression
75 ft
Angle of Elevation
A group of hikers on a camping trip climb to the top of a 1500-foot mountain. When the hikers look down at an angle of depression of 36º, they can see the campsite in the distance. What is the horizontal distance between the campsite and the group to the nearest foot?
A ground crew worker who is 6 feet tall is directing a plane on the runway. The worker sights the plane at an angle of elevation of 32º. If the plane is 150 feet off the ground, what is the horizontal distance, also called the ground distance, from the worker to the plane?
September 23, 2016
The legs of an isosceles are each 21 cm long and the angle between them has a measure of 52 degrees. What is the legth of the third side?
A student looks out of a second story school window and sees the top of the school flagpole at an angle of elevation of 22 degrees. The student is 18 ft above the ground and 50 feet from the flagpole. Find the height of the flagpole.
Sketch the circle Sketch the two tangents to the circle from the origin. Find the measures of the angle between tangents.
Applications of Inverse Functions Day 2 Solve the Right Triangle
35
September 23, 2016
A hot air balloon that is moving above a neighborhood has an angle of depression of 28 degrees to one house and 52 degrees to the house down the street. If the height of the balloon is 650 feet, estimate the distance between the two houses.
The angle of elevation from a car to the top of an apartment building is 45 degrees. If the angle of elevation from the car that is 22 feet directly in front of the first car is 64 degrees, how tall is the building?
Inverse Functions
Inverse Functions and
Applications
Algebraically:
or
Verbally: they both mean - find the angle whose sin is Numerically: The answer.
Numerical 1)
2)
September 23, 2016
3)
4)
5) Find the value of 5
6) Find the value of
7
9 4
September 23, 2016
7) Find the value of
8) Find the value of 50 16 33
Find the value of x. All angles given in degrees.
10)
9) x
25 43
10
x 37
Solve the triangle. 11) x
17
40
September 23, 2016
Find the missing side -
Find the missing side -
80
9
x
x
APPLICATION
Using the Inverse Function
A competitor in a triathlon is running along the course shown. Determine the length in feet that the runner must cover to reach the finish line. Runner
200 ft
Finish Line
September 23, 2016
Suppose a competitor in the swimming portion of the race is swimming along the course shown. Find the distance the competitor must swim to reach the shore.
Swimmer
Finish Line
Angle of depression and angle of elevation
Angle of Depression
75 ft
Angle of Elevation
A group of hikers on a camping trip climb to the top of a 1500-foot mountain. When the hikers look down at an angle of depression of 36º, they can see the campsite in the distance. What is the horizontal distance between the campsite and the group to the nearest foot?
A ground crew worker who is 6 feet tall is directing a plane on the runway. The worker sights the plane at an angle of elevation of 32º. If the plane is 150 feet off the ground, what is the horizontal distance, also called the ground distance, from the worker to the plane?
September 23, 2016
The legs of an isosceles are each 21 cm long and the angle between them has a measure of 52 degrees. What is the legth of the third side?
A student looks out of a second story school window and sees the top of the school flagpole at an angle of elevation of 22 degrees. The student is 18 ft above the ground and 50 feet from the flagpole. Find the height of the flagpole.
Sketch the circle Sketch the two tangents to the circle from the origin. Find the measures of the angle between tangents.
Applications of Inverse Functions Day 2 Solve the Right Triangle
35
September 23, 2016
A hot air balloon that is moving above a neighborhood has an angle of depression of 28 degrees to one house and 52 degrees to the house down the street. If the height of the balloon is 650 feet, estimate the distance between the two houses.
The angle of elevation from a car to the top of an apartment building is 45 degrees. If the angle of elevation from the car that is 22 feet directly in front of the first car is 64 degrees, how tall is the building?
