Questions: Determine the length of side x. Round your answer to the nearest tenth, if necessary.

Transcript text: Determine the length of side $x$. Round your answer to the nearest tenth, if necessary.

Solution

Solution Steps

Step 1: Identify the given information

We are given a right triangle with one angle of 30°, the hypotenuse of 25, and we need to find the length of the side opposite the 30° angle (denoted as $ x $).

Step 2: Use the sine function

In a right triangle, the sine of an angle is the ratio of the length of the opposite side to the hypotenuse. Therefore, we can use the sine function: \[ \sin(30°) = \frac{\text{opposite}}{\text{hypotenuse}} \]

Step 3: Substitute the known values

Substitute the known values into the sine function: \[ \sin(30°) = \frac{x}{25} \]

Step 4: Solve for $ x $

We know that $ \sin(30°) = 0.5 $. Therefore: \[ 0.5 = \frac{x}{25} \] \[ x = 0.5 \times 25 \] \[ x = 12.5 \]