Question

In a right triangle ABC with angle A equal to 90o, find angle B and C so that sin(B) = cos(B).

Answer 1

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Answer 2

The angle C and B = 45°

Given:

In a right angled triangle ABC with  ∠A = 90°

∠ B and ∠C are be the remaining angles

and sin(B) = cos(B)

To find:

Find angle B and C

Solution:  

As we know in a right angle triangle

Sin θ = opposite/ hypotenuse    

Cos θ = Adjacent/ hypotenuse

From Right angle triangle ABC

Sin B = AC / BC  

Cos B = AB / BC

Given that  sin(B) = cos(B)

⇒ $\frac{AC}{BC} = \frac{AB}{BC}$  

⇒ AC = AB from this we can conclude that  ∠ACB = ∠ABC

Therefore, The angles ∠C = ∠B

As we know Sum of angles in triangle = 180°

⇒ ∠A  + ∠B + ∠C = 180°

⇒ 90° + ∠B + ∠B = 180°

⇒ 2 ∠B = 90°

⇒  ∠B = 45°  

⇒  ∠C = 45°  

The angle C and B = 45°

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