Question

A, B & C form the vertices of a triangle, where ∠CAB = 90°.AB = 10.5 m and AC = 5.2 m.

Evaluate ∠CBA, giving your answer rounded to 3 SF.

Answer 1

Answer: In a right-angled triangle, we can use the Pythagorean Theorem to find the length of the remaining side. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the length of side BC can be found using the Pythagorean Theorem:

BC^2 = AB^2 + AC^2

BC^2 = 10.5^2 + 5.2^2

BC^2 = 110.25 + 27.04

BC^2 = 137.29

BC = √137.29

BC ≈ 11.68 m

Now that we have the length of side BC, we can use the inverse cosine function (cos^-1) to find the angle ∠CBA:

∠CBA = cos^-1 (BC / AB)

∠CBA = cos^-1 (11.68 / 10.5)

∠CBA ≈ 68.194°

Rounding to 3 significant figures, the answer is ∠CBA = 68.2°.

Explanation: