A tunnel has a semi-circular cross-section and a diameter of 10 m. If the roof of the bus just touches the roof of the tunnel when the bus is 2 m from one side, how high is the bus?
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Step-by-step explanation:
1. Any line from the centre of the circle to a point at the circumference is the radius.
2. We can find the missing length of a right angle triangle by using the Pythagoras theorem.
3. Pythagoras theorem state that a^2 + b^2 = c^2
* See attached for the visual interpretation of the question.
Find the length BC:
BC = (10 - 2 - 2) \div 2
BC = 3 m
Find the radius of the semicircle:
Diameter = 10m
Radius = Diameter \div 2
Radius = 5 m
Radius is 5m:
AB = Radius
AB = 5m
Find height AB:
a^2 + b^2 = c^2
height^2 + BC^2 = AB^2
height^2 = AB^2 - BC^2
height^2 = 5^2 - 3^2
height^2 = 16
height = \sqrt{16}
height = 4
Answer: The height of the bus is 4 m tall.
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