Question

In the given right angle triangle, if Sin$\theta$ =$\frac{3}{5}$

The value of 3tan$\alpha$ is :

• A. 3
• B. 4
• C. 5
• D. 6

Answer 1

The correct option is B

4

Sin$\theta$ = $\frac{3}{5}$ i.e. Let BC=3x and AC=5x.

Without loss of generality, let us take x = 1 so that BC = 3, AC = 5.

By Pythagoras theorem we know that

$A{C}^2$=$A{B}^2$+$B{C}^2$

So, $5^2$= $A{B}^2$ + $3^2$

$\to$ $A{B}^2$ = $5^2$ - $3^2$

$\to$ AB = $(16{)}^{0.5}$ = 4

Since AB = 4 and BC = 3

tan$\alpha$ = $\frac{AB}{BC}$

$\therefore$ 3tan$\alpha$ = 3$\times$$\frac{4}{3}$ = 4