Question

The side opposite the right-angle measures 4 in. What is the measurement of the side opposite the 30 degree angle? Draw and label the triangle before solving.

Answer 1

2 inches.

Step-by-step explanation:

In a right triangle:

• The side opposite the right angle = 4 inches

,

• Let the side opposite the 30 degrees angle = x.

Note that the side opposite the right angle is always the hypotenuse.

The diagram is drawn and attached below:

Next, we solve for x.

From trigonometrical ratios:

`\begin{gathered} \sin \theta=\frac{\text{Opposite side length to }\theta}{\text{Length of the Hypotenuse}} \\ \implies\sin 30\degree=(x)/(4) \end{gathered}`

Cross multiply.

`\begin{gathered} x=4*\sin 30\degree \\ x=4*0.5 \\ x=2\text{ inches} \end{gathered}`

The measurement of the side opposite the 30-degree angle is 2 inches.