Question

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

Answer 1

SOLUTION :                                    

Given : In a right ∆ ABC, ∠C = 90° ,if ∠B = 60° and AB = 15 units.

In ∆ABC,  

∠A + ∠B + ∠C = 180°

[Sum of angles in a ∆ = 180°]

∠A + 60° + 90° = 180°  

∠A + 150°  = 180°  

∠A = 180° - 150°

∠A = 30°  

In ∆ABC,  

With reference to ∠B ,  

Base = BC , Perpendicular = AC , Hypotenuse = AB

cos 60° = B/ H = BC/AB

½ = BC/15

2BC = 15  

BC = 15/2

BC = 7.5 units

sin 60° = P/H = AC/AB  

√3/2 = AC/15

2AC = 15√3

AC = (15√3) /2 units

Hence, ∠A = 30°, BC = 7.5 units ,AC = (15√3) /2 units

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Answer 2

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