Question

solve for x. round to the nearest tenth, if necessary. triangle image with right angle at u, side ut = 1, angle at t is 50 degrees, side uv = x

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle at $U$, angle at $T$ is $50^\circ$. Side $x$ is opposite to $50^\circ$, side length 1 is adjacent to $50^\circ$. Use tangent ratio: $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$

Step2: Substitute values into formula

$\tan(50^\circ)=\frac{x}{1}$

Step3: Solve for $x$

$x = \tan(50^\circ)$
Calculate $\tan(50^\circ)\approx1.1918$, round to nearest tenth: $x\approx1.2$

Answer:

$1.2$