Question

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?

Answer 1

Recall that:

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.