Question

the London eye is 135m at it's highest point. At it's lowest point it is about 3m off the ground. It takes about 30 minutes to revolve entirely. Across the river, Big Ben is about 96m tall. If you were to take a ride on the London eye, for how long were you higher than Big Ben?

Answer 1

This is the concept of trigonometric identities;
To solve the expression we proceed as follows, first we simplify the question, we subtract 3 m from 135m and 96m. Our new height for London eye is 132m and Big Ben is 93 m.
speed is given by:
1 rev/min= 2pi rad/min
thus our speed will be:
1/30 rev/min
=pi/15 rad/min
Subtracting 93 m (Big Ben)- 66 m (radius of the London Eye)= 27 m
This will make right angle as:
adjacent=27 m
hypotenuse=66 m
cos x=27/66=9/22
x=arccos(9/22)

Therefore the time taken will be given by:
2 cos^-1 (9/22)* (15/pi min/rad)
N/B the 2 accounts for both up and down
thus time taken will be:
30*cos^-1(9/22)
=30cos^-1 (9/22) min