Height of a Ferris Wheel Car A model for the height \(h\) (in feet) of a Ferris wheel car is \(h = 50 + 50 \sin 8 \pi t\) where \(t\) is the time (in minutes). (The Ferris wheel has a radius of \(50\) feet.) This model yields a height of \(50\) feet when \(t = 0\) . Alter the model so that the height of the car is \(1\) foot when \(t = 0\) .

\(h = 51 - 50 \sin ( 8 \pi t + \frac { \pi } { 2 } )\)

A rabbit is hopping along a garden path at the same time that a bird takes off from the ground and travels \( 425 m \) in a northeasterly direction. What is the angle of elevation between the bird and the rabbit after the rabbit has hopped \( 320 m \) ?

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When the sun's angle of elevation is \( 38 \) degrees, a building casts a shadow of \( 45 m \) . How high is the building?

____meters

An advertising blimp hovers over the football stadium in Detroit, where a very lovely geometry teacher is watching the Green Bay Packers play the Detroit Lions. The pilot of the blimp sights the very lovely geometry teacher at an angle of depression of \( 8 \) degrees. Find the distance between the pilot and the very lovely geometry teacher, if the pilot is waving from an altitude of \( 125 m \) .

____meters

A person who is \( 1.5 m \) tall is standing \( 20 m \) from the base of a building. The person sights the top of the building with an angle of elevation of \( 58 \) degrees. Find the height of the building to the nearest meter. (Hint: think about what you need to do with the person's height.)

____meters

What is the distance from Kareem to the house?

Kareem and Amy are standing on a riverbank, \( 150 \) meters apart, at points \( A \) and \( B \) respectively. (See the figure below.) They want to know the distance from Kareem to a house located across the river at point \( C \) . Kareem measures angle \( A \) (angle \( B A C \) ) to be \( 55 ^ { \circ } \) , and Amy measures angle \( B \) (angle \( A B C \) ) to be \( 74 ^ { \circ } \) . What is the distance from Kareem to the house? Round your answer to the nearest tenth of a meter.