Question

The smallest side of right-angled triangle has length $2cm$. The tangent of one acute angle is $\frac{3}{4}$. What is the hypotenuse of the triangle?

• A. $5cm$
• B. $2.5cm$
• C. $1.25cm$
• D. $\frac{10}{3}cm$

Answer 1

The correct option is D $\frac{10}{3}cm$

$\tan \theta =\frac{3}{4}$ so $\sin \theta =\frac{3}{5}$
$\Rightarrow \frac{2}{x}=\frac{3}{5}$ so $x=\frac{10}{3}cm$