Question

A, B & C form the vertices of a triangle, where

∠
CAB = 90°.
AB = 10.6 m and AC = 5.8m.
Evaluate
∠
ACB, giving your answer rounded to 3 SF.

Answer 1

We can use the trigonometric function of sine to find the measure of angle ACB.

First, we note that sin(ACB) = opposite/hypotenuse = BC/AB.

To find BC, we use the Pythagorean theorem:

BC^2 = AB^2 - AC^2

BC^2 = (10.6 m)^2 - (5.8 m)^2

BC^2 = 67.24 m^2 - 33.64 m^2

BC^2 = 33.6 m^2

BC = sqrt(33.6) m

BC = 5.8 m (rounded to 1 decimal place)

Therefore, sin(ACB) = BC/AB = 5.8/10.6 = 0.5472

Using the inverse sine function on a calculator, we find:

ACB = sin^-1(0.5472)

ACB = 33.11°

Therefore, the measure of angle ACB is 33.11 degrees, rounded to 3 significant figures.