Applying and analysing trigonometric functions

From an observation point 20 ft from the base of a geyser, the angle of elevation to the top of the geyser is  $50^{\degree}$  . To the nearest foot, how tall is the geyser?

A Ferris wheel is 5 feet off the ground and has a diameter of 40 feet. You get on and find that it takes 30 seconds to complete one revolution. Write an equation that models your height, y, as a function of time, x.

• y = 20cos(pi/15 x) + 5

• y = -20cos(pi/15 x) + 5

• y = 40cos(pi/30 x) + 5

• y = -40cos(pi/30 x) + 5

• y = -20cos(pi/30 x) + 5

A yacht is anchored 90 feet offshore from the base of a lighthouse.  The angle of elevation from the boat to the top of the lighthouse is 26 degrees.  The distance between the yacht and the top of the lighthouse is about 100 feet.  Which of these is nearest to the height of the lighthouse? 

• 25 feet
• 45 feet 
• 110 feet 
• 135 feet 

What is the amplitude of the Ferris wheel?

• 6

• 1

• 3

• 7

Raya is riding a Ferris wheel with a radius of 50 meters and a center 65 meters off the ground. Assume Raya starts at the right-hand side of the Ferris wheel.

Find Raya's height after the wheel rotates $310^{\circ}$ 

• about 43 meters

• about -38 meters

• about 27 meters

• about 108 meters

A central angle measure 4.5 radians and has an arc of 35 inches. What is the radius of the circle?

• 7.78 inches

• 8.21 inches

• 157.5 inches

• 7 inches

 $h\left(t\right)\ =\ 60\sin\left(\frac{2\pi t}{10}\right)\ +\ 80$ 

The height in feet of one of the passenger seats on the Ferris wheel can be modeled by the the given function.

What is the DIAMETER of the Ferris wheel?

• 60 feet
  

• 80 feet
  

• 120 feet
  

• 160 feet
  

 $h\ =\ 24\sin\left(\frac{2\pi t}{0.2}-\frac{\pi}{2}\right)\ +\ 24$ 

A piece of gum is stuck on a bike wheel. The gum's height, in inches is given by the function, where t is the number of seconds.

Which statements are true about the gum's height? Select ALL.

• The difference between the highest and lowest point of the gum is 24 inches
  

• The difference between the highest and lowest point of the gum is 48 inches

• The gum starts at its highest point on the tire.
  

• The gum starts at its lowest point on the tire.
  

Tom is riding a Ferris wheel with a radius of 45 meters and a center 51 meters off the ground. Assume Tom starts at the right-hand side of the Ferris wheel and it rotates counter-clockwise. 

Find Tom's height after the wheel rotates  $113^{\circ}$  

• about 92 meters

• about 47 meters
  

• about 41 meters

• about -4 meters

A ferris wheel has a diameter of 400ft and has a platform that is 20ft off the ground. It takes two minutes for a full revolutions. What equation models the height of person as they ride the ferris wheel if at time = 0 min they where at the 3 o'clock position and ferris wheel travels counterclockwise.

• $f\left(x\right)=\ 200\sin\left(\pi x\right)+220$

• $f\left(x\right)=\ -200\sin\left(\pi x\right)+220$

• $f\left(x\right)=-200\sin\left(2x\right)+220$

• $f\left(x\right)=\ 200\sin\left(2x\right)+220$