Question

3)
in a right triangle, one acute angle is 47°, the side length adjacent to this angle is 10, and the side length opposite to this angle is x.

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle, with angle $47^\circ$, opposite side to this angle is $10$, and adjacent side is $x$. Use tangent function: $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$

Step2: Substitute known values

$\tan(47^\circ)=\frac{10}{x}$

Step3: Solve for $x$

Rearrange to isolate $x$: $x=\frac{10}{\tan(47^\circ)}$
Use $\tan(47^\circ)\approx1.0724$, so $x\approx\frac{10}{1.0724}$

Answer:

$x\approx9.32$