Question

If sin θ = `5/13` and AC = 52 cm, find AB, BC and tan θ.

Answer 1

Given:

sin θ = `5/13`

AC = 52 cm (hypotenuse)

Triangle ABC, with a right angle at B and angle θ at A.

We need to find:

AB (opposite side to θ)

BC (adjacent side to θ)

tan θ

Step 1: Understand the ratio from sin θ

Sin θ `"opposite"/"hypotenuse" = (AB)/(AC) = 5/13`

AB : BC : AC = 5 : 12 : 13

Step 2: Use the given hypotenuse to find AB and BC

Since the full triangle is in the ratio 5:12:13 and AC = 13 parts = 52 cm

`1 52/13 = 4`cm

AB = 5 parts = 5 × 4 = 20 cm

BC = 12 parts = 12 × 4 = 48 cm

tan θ `"opposite"/"adjacent" = (AB)/(BC) = 20/48`

= `5/12`