Question

find the value of x.
triangle with hypotenuse 15, angle 35° at the base, right angle, and height x
x is blank
(round to the nearest tenth as needed.)

Explanation:

Step1: Identify trigonometric ratio

We use the sine function: $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$, where $\theta=35^\circ$, opposite side is $x$, hypotenuse is 15.

Step2: Rearrange to solve for x

$x = 15 \times \sin(35^\circ)$

Step3: Calculate the value

First, $\sin(35^\circ) \approx 0.5736$, so $x \approx 15 \times 0.5736 = 8.604$

Step4: Round to nearest tenth

Round 8.604 to one decimal place.

Answer:

8.6