Question

In ΔABC, ∠B = 90°, ∠C = 30° and AC = 16 cm. Find the lengths of AB and BC.

Answer 1

Given:

In △ABC

∠B = 90°

∠C = 30°

AC = 16 cm

Finding AB and BC.

Step 1:

∠A = 180° − ∠B − ∠C

= 180° − 90° − 30°

= 60°

Step 2:

∠B = 90°

Hypotenuse: AC = 16

AB: opposite to ∠C = 30°

BC: adjacent to ∠C = 30°

sin(30°) = `"opposite"/"hypotenuse" = (AB)/(AC)`

sin(30°) = `(AB)/(AC)`

sin(30°) = `(AB)/(16)`

`1/2 = (AB)/16`

AB = 8 cm

cos (30°) = `"adjacent"/"hypotenuse" = (BC)/(AC)`

cos(30°) = `(BC)/16`

`sqrt3/2 = (BC)/16`

`BC = 16 ⋅ sqrt3/2`

`BC = 8sqrt3 "cm"`