Question

$\Delta ABC$ is right angled at C with sides AB = 10 cm and AC = 6 cm. Find tan B.

• A. $\frac{3}{4}$
• B. $\frac{8}{6}$
• C. $\frac{6}{10}$
• D. $\frac{8}{10}$

Answer 1

The correct option is A

$\frac{3}{4}$

$In\Delta ABC,AB=10cm,AC=6cm$

Applying Pythagoras' theorem to $\Delta ABC$, we have,

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

$6^2+B{C}^2={10}^2$

$⟹B{C}^2=100-36$

$⟹BC=\sqrt{64}=8cm$

The tangent of an angle is the ratio of the length of the opposite side(perpendicular) to the length of the adjacent side(base).

$\therefore tan\left(\angle B\right)=\frac{AC}{BC}=\frac{6}{8}=\frac{3}{4}$