Question

select the correct answer.
what is the value of x?
（there is a right triangle in the picture, with one acute angle of 45°, the hypotenuse is 15, and the right side is x.）
a. 10.6
b. 15
c. 21.2
d. 7.5

Explanation:

Step1: Identify triangle type

This is a right isosceles triangle (one right angle, one 45° angle, so the third angle is also 45°). The side opposite the 45° angle (length 15) is the hypotenuse, and $x$ is one of the equal legs.

Step2: Use trigonometric ratio

We use $\sin(45^\circ) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{x}{15}$. Since $\sin(45^\circ) = \frac{\sqrt{2}}{2}$, rearrange to solve for $x$:
$x = 15 \times \sin(45^\circ) = 15 \times \frac{\sqrt{2}}{2}$

Step3: Calculate numerical value

$\sqrt{2} \approx 1.414$, so $x \approx 15 \times \frac{1.414}{2} = 15 \times 0.707 = 10.605$

Answer:

A. 10.6