Question

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

∠CAB = 90°.
AB = 10.2 m and AC = 4.9m. Evaluate
∠ ACB, giving your answer rounded to 3 SF.

Answer 1

Step-by-step explanation: To find the measure of angle ACB, we can use the Pythagorean Theorem: AB^2 + AC^2 = BC^2.

Substituting in the given values for AB and AC, we get: 10.2^2 + 4.9^2 = BC^2

Solving for BC, we get: BC = √(10.2^2 + 4.9^2)

Substituting this value back into the equation for the Pythagorean Theorem, we get:

AB^2 + AC^2 = (√(10.2^2 + 4.9^2))^2

Simplifying this equation, we get:

AB^2 + AC^2 = 10.2^2 + 4.9^2

This equation is already in the correct form, so we can solve for ∠ACB directly:

∠ACB = tan^-1(AC/AB)

Substituting in the given values for AC and AB, we get:

∠ACB = tan^-1(4.9/10.2)

Using a calculator, we find that tan^-1(4.9/10.2) is approximately equal to 26.7°.

Rounded to 3 significant figures, this value is 26.7°.