Questions: Solve for x. Round to the nearest hundredth.

Transcript text: Solve for $x$. Round to the nearest hundredth.

Solution

Solution Steps

Step 1: Identify the right triangle and given sides

The problem involves a right triangle with one leg measuring 9 cm and the hypotenuse measuring 17 cm. We need to find the angle $ 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. Here, the opposite side to angle $ x $ is 9 cm, and the hypotenuse is 17 cm. Therefore, we use the sine function: \[ \sin(x) = \frac{9}{17} \]

Step 3: Calculate the angle using the inverse sine function

To find the angle $ x $, we take the inverse sine (arcsine) of $ \frac{9}{17} $: \[ x = \sin^{-1}\left(\frac{9}{17}\right) \]

Step 4: Compute the value

Using a calculator: \[ x \approx \sin^{-1}(0.5294) \approx 31.03^\circ \]