Question

If ∆ABC is a right triangle such that ∠C = 90°, ∠A = 45° and BC = 7 units. Find ∠B, AB and AC.

Answer 1

SOLUTION :                                    

Given : In a right ∆ ABC, ∠C = 90° ,if ∠A = 45° and BC = 7 units.

In ∆ABC,  

∠A + ∠B + ∠C = 180°

[Sum of angles in a ∆ = 180°]

45°  + ∠B + 90° = 180°  

∠B + 135°  = 180°  

∠B = 180° - 135°

∠B = 45°

Hence, ∠B = 45°

In ∆ABC,  

With reference to ∠B ,  

Base = BC , Perpendicular = AC , Hypotenuse = AB

cos 45° = B/ H = BC/AB

1/√2 = 7/AB

AB = 7√2 units

sin 45° = P/H = AC/AB  

1/√2  = AC/7√2

AC = (7√2) /√2

AC = 7 units

Hence, the value of ∠B = 45° , AC = 7 units and AB = 7√2 units

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