Question

Label the lengths of the two missing sides in thisright triangle.1530°--111:: 513:: 1073:: 1513:: 30

Answer 1

The given triangle is a right angle triangle, so side opposite to the right angle is always hypotenues.

By using the trigonometric ratio finding the perpendicular,

$\tan 30^{\circ}=\frac{perpendicular\text{ }}{base}$

Here, perpendicular is the side opposite to the angle given is 30 degree.

$\frac{1}{\sqrt[]{3}}=\frac{P}{15}$$P=\frac{15}{\sqrt[]{3}}$

Now, finding the third side by using Pythagorean theorem

$\text{Hypotenues}^2=Perpendicular^2+Base^2$

Here, Base = 15 (given)

$\begin{gathered} H^2=(\frac{15}{\sqrt[]{3}})^2+(15)^2 \\ =\frac{225}{3}+225 \\ =\frac{225+675}{3} \\ =300 \\ H=10\sqrt[]{3} \end{gathered}$

Thus, the correct answer is (2)