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}}=(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 \\ =(225)/(3)+225 \\ =(225+675)/(3) \\ =300 \\ H=10\sqrt[]{3} \end{gathered}`

Thus, the correct answer is (2)