Question

find the value of tan theta, by the following figure



please help...​

Answer 1

Answer: (A) √3

Step-by-step explanation:

From the figure, ∆ADB, <D is right angle which is 90°.

Using, Pythagoras Theorem,

AD² + DB² = AB²

AD² + (9)² = (18)²

(DB=9 & AB=18 given in figure)

AD² = (18)² - (9)²

AD² = (18+9) (18-9)

(using (a²-b²) = (a+b)(a-b) )

AD² = 27 (9)

AD² = (9×3) (9)

AD² = 9² ×3¹

AD = 9 √3

(By taking Square root)

Now, using Trigonometry

Tan¢ = CD/AD

Tan¢ = 27/9√3

Tan¢ = 3/√3

Tan¢ = √3