Question

Using ruler and compasses only, construct a $△ABC$ having given $\angle ABC={60}^0,\angle ACB={45}^0$ and the perpendicular from $A$ to $BC$ equal to $2.5$ cm. The length of $AB$ is

• A. $2.1$ cm
• B. $2.9$ cm
• C. $3.5$ cm
• D. $4.2$ cm

Answer 1

Answer: (B)

$2.9$ cm

Draw a line segment $BC$ of any length.

Now, make a line segment from $B$ such that $\angle ABC={60}^0$ and also, make another line from $C$ such that $\angle ACB={45}^o$

Then, draw a perpendicular $AD$ of $2.5$ cm from $A$ to $BC$

Now, $\sin {60}^o=\frac{2.5}{x}$

$\Rightarrow \frac{\sqrt{3}}{2}=\frac{2.5}{x}$

$\Rightarrow x=\frac{5}{\sqrt{3}}=2.9cm$

Hence, (B) is the correct answer.