Question

In a right triangle ABC, right angled at C, if ∠B = 60° and AB = 15units, find the remaining angles and sides.

Answer 1

∠B = 60°
∠C = 90°     ...(Since triangle ABC is right angled at C)
∠A + ∠B + ∠C = 180°
∠A  + 60° + 90° =180°
∠A = 180° - 150°
∠A = 30°
Now,

sin60° = `"AC"/"AB"`
AC = sin60° x AB

AC = `sqrt(3)/(2) xx 15`

AC = `(15sqrt(3))/(2)"units"`
Also,

cos60° = `"BC"/"AB"`
BC = cos60° x AB
BC = `(1)/(2) xx 15`
BC = 7.5units.