Functions (trigonometric)

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.   Which of these is nearest to the height of the lighthouse? 

• 25 feet
• 44 feet 
• 81 feet 
• 185 feet 

Sally is flying a kite at an angle of 41 degrees. If the kite is 10 feet up in the air, how long is the kite string? 

• 6.6 feet
• 10.3 feet
• 15.2 feet
• 20 feet

The center of a windmill is 5 feet off the ground. The blades extend 1.5 meters from the center. The windmill rotates clockwise. Which equation represents the height of point W as the windmill rotates around?

• h = 1.5sinθ + 5

• h = -1.5sinθ + 5

• h = 5sinθ + 1.5

• h = -5sinθ + 1.5

A 1.5m tall boy stands at a distance of 45 m from a tower. The angle of elevation from his eyes to the top of the tower is 30 degrees . Find the height of the tower.

•  $\left(1.5\ +\ 15\sqrt{3}\right)\ m$  

•  $15\sqrt{3}\ m$  

•  $\left(15\sqrt{3}\ -\ 1.5\right)m$  

• 46 m 

A cathedral window is built in the shape of a semicircle. If the window is to contain three stained glass sections of EQUAL SIZE, what is the area of the YELLOW SECTOR?

• 3.3 ft²

• 4.5 ft²

• 6.3 ft²

• 7.1 ft²

A ferris wheel has a radius of 100ft and has a platform that is 10ft off the ground. It takes 6 minutes for two full revolutions. What equation models the height of person as they ride the ferris wheel if at time = 0 min they where at the 9 o'clock position and ferris wheel travels counterclockwise.

•  $f\left(x\right)=\ -100\sin\left(\frac{2\pi}{3}x\right)+110$ 

•  $f\left(x\right)=\ 100\sin\left(\frac{2\pi}{3}x\right)+110$ 

•  $f\left(x\right)=-50\sin\left(3x\right)+55$ 

•  $f\left(x\right)=\ 50\sin\left(3x\right)+55$ 

A 4 ft tall child creates a shadow that is 7.5 ft long. What is the angle of elevation of the sun? 

• 62 degrees
• 49 degrees
• 28 degrees
• 15 degrees

The equation represents the height of a passenger on a Ferris wheel (in feet) as a function of time (in seconds)

 $h=56+29\sin\left(8t\right)$  
FInd the height of the passenger after the wheel rotates 160 degrees.

• 46.08 ft

• 65.92 ft

• 78.85 ft

• 20 ft

Kiara's 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.Find the height of the lighthouse.

• 25 feet

• 45 feet

• 110 feet

• 135 feet

What is the maximum height on the Ferris wheel?

• 1 meter

• 4 meters

• 7 meters

• 24 meters