SOLUTION: A brick 4 cm high is placed to stop a wheel of the car. Upper face of the brick is 8 cm away from the point where the wheel touches the road.find the diameter and area of the whe

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Question 1006244: A brick 4 cm high is placed to stop a wheel of the car. Upper face of the brick is
8 cm away from the point where the wheel touches the road.find the diameter and
area of the wheel.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!


sin(∠ACB) = 4/8 = 1/2

therefore ∠ACB = 30°

Therefore since ∠BCO = 90°, ∠ACO = 60°

Therefore ΔOAC is an equilateral triangle because the two radii, 
OA and OC are equal, making it isosceles, and it has one 60° angle.  

So all the sides of ΔOAC are equal, so OC=8.

So the radius of the wheel is 8, its diameter is 16 and its
area is

pr² = p(8)² = 64p.

Edwin