Question

if √3 tan A = 2 cos B = 1, then find the value of angle C?​

Answer 1

Answer:

tanA=1/√3

A=30°

cosB=1/2

B=60°

we know that,

sum of angles in triangle=180°

A+B+C=180°

30+60+C=180°

C=90°

Answer 2

Angle C = 90°

GIVEN:

√3 tan A = 2 cos B = 1

TO FIND:

The angle of C

SOLUTION:

Given that √3 tan A = 2 cos B = 1

Take √3 tan A = 1

⇒ tan A = 1/√3 _ (1)

As we know from trigonometric table tan 30 = 1/√3

⇒ tan A = tan 30°

⇒ A = 30°

Take 2 cos B = 1

⇒ cos B = 1/2

from trigonometric table  cos 60° = 1/2

⇒ cos B = cos 60°

⇒ B = 60°

As we know In a triangle sum of angles = 180°

⇒ A + B + C = 180°

⇒ 30°+60°+ C = 180°

⇒ C = 180°- 90° = 90°

Therefore, Angle C = 90°

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