Question

1. in a right triangle, one acute angle is 49°, the length of one leg is 11, find the length of the other leg marked as x.

Explanation:

Step1: Identify trigonometric ratio

For the $49^\circ$ angle, the side opposite is 11, and $x$ is the adjacent side. We use the tangent ratio: $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$

Step2: Substitute known values

$\tan(49^\circ)=\frac{11}{x}$

Step3: Rearrange to solve for $x$

$x=\frac{11}{\tan(49^\circ)}$

Step4: Calculate the value

Using $\tan(49^\circ)\approx1.1504$, we get $x\approx\frac{11}{1.1504}\approx9.56$

Answer:

$x\approx9.6$ (rounded to one decimal place, or $x=\frac{11}{\tan(49^\circ)}$ for the exact value)