ΔABC is right angled at B. If ∠A = 30°, what is the length of AB (in cm), if AC = 10 cm?

Answer: Option B

Solution

Answer: Option B

Solution:

$$\begin{array}{rl}& \text{Given,}\\ & \angle A=30^{\circ }\\ & \therefore \angle C=60^{\circ }\\ & \left(\tan {60}^{\circ }=\frac{\sqrt{3}}{1}=\frac{AB}{BC}\right)\\ & AB=\sqrt{3},BC=1\\ & \therefore AC=\sqrt{A{B}^2+B{C}^2}\\ & =\sqrt{\left({\left(\sqrt{3}\right)}^2+{\left(1\right)}^2\right)}\\ & =2\text{unit}\\ & 2\text{unit}=10\text{cm}\\ & 1\text{unit}=5\text{ cm}\\ & \boxed{AB=\sqrt{3}\text{ unit}=5\sqrt{3}}\end{array}$$