Question

If cos θ = 0.96 and AB = 24 cm, find BC, AC and cot θ.

Answer 1

Given:

cos θ = 0.96

AB = 24 cm (adjacent to angle θ)

Triangle ABC, right-angled at B, with angle θ at A

Need to find:

BC (opposite side to θ)

AC (hypotenuse)

cot θ

Step 1: Use the definition of cosine

cos θ `"adjacent"/"hypotenuse" = (AB)/(AC) ⇒ 0.96 = 24/(AC)`

AC = `24/0.96` = 25 cm

Step 2: Use the Pythagoras Theorem to find BC

AC² = AB² + BC²

= 25² = 24² + BC² = 625

= 576 + BC² = 49

= BC² `sqrt49` = 7cm

Step 3: Find cot θ

cot θ `"adjacent"/"opposit" = (AB)/(BC) = 24/7`