Question

In the right-angled triangle ABC in Fig. 4.3, B = 90° and the lengths of AB and BC are given to the nearest centimetre. Calculate AC. ​

Answer 1

|AC| = 132 cm (nearest centimetre)

Explanation:

Pythagoras Theorem

Pythagoras Theorem explains the relationship between the three sides of a right triangle. The formula is:

`\large\boxed{c^2=a^2+b^2}`

where:

• a and b are the legs of the right triangle
• c is the hypotenuse (longest side) of the right triangle.

From inspection of the given right triangle:

• a = AB = 45 cm
• b = BC = 124 cm
• c = AC

Substitute the given values into the formula and solve for AC:

`\begin{aligned}c^2 & = a^2+b^2 &\\\\\implies AC^2&=AB^2+BC^2\\ AC^2&=45^2+124^2\\ AC^2&=2025+15376 \\ AC^2&=17401\\√( AC^2)&=√( 17401)\\ AC&=131.91285\\AC&=132\; \sf cm \; (nearest\;centimetre)\end{aligned}`

Therefore, |AC| is 132 cm to the nearest centimetre.