Question

in the given figure, find the value of tan theta.​

Answer 1

• in the given figure, the value of tan θ is equal to √3 .

Correct Question :- Refer to image.

Formula used :-

• In a right angled triangle, according to pythagoras theorem we have :- (Base)² + (Perpendicular)² = (Hypotenuse)² .
• tan θ = Perpendicular / Base. { Where perpendicular is opposite to θ . }

Solution :-

since AD ⟂ CB,

→ ∠ADB = ∠ADC = 90°

So, in right angled ∆ADB we have,

→ AD² + DB² = AB² { By pythagoras theorem }

putting given values of DB = 9 and AB = 18 we get,

→ AD² + (9)² = (18)²

→ AD² + 81 = 324

→ AD² = 324 - 81

→ AD² = 243

→ AD² = 3 × 9 × 9

→ AD² = 3 × 9²

Square root both sides,

→ AD = 9√3 -------- Equation (1)

Now, in right angled ∆ADC we have,

→ Tan θ = Perpendicular / Base

→ Tan θ = CD/AD

putting given value of CD = 27 and value of AD from Equation (1) we get,

→ Tan θ = (27/9√3)

→ Tan θ = (3/√3)

→ Tan θ = (√3 × √3)/√3

→ Tan θ = √3 (Ans.)

Hence, the value of tan θ is equal to √3 .

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