Question

1. -/1 points find x rounded to one decimal place. x = show my work (optional) submit answer

Explanation:

Step1: Find left - hand side length

Let the length of the left - hand side of the big right - triangle (adjacent to the 60° angle) be $a$. In the left - hand right - triangle with height 50 and angle 60°, we use the tangent function $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. So, $\tan60^{\circ}=\frac{50}{a}$, and since $\tan60^{\circ}=\sqrt{3}$, we have $a = \frac{50}{\sqrt{3}}=\frac{50\sqrt{3}}{3}$.

Step2: Find right - hand side length

In the right - hand right - triangle with height 50 and angle 30°, we use the tangent function again. $\tan30^{\circ}=\frac{50}{b}$, and since $\tan30^{\circ}=\frac{1}{\sqrt{3}}$, we have $b = 50\sqrt{3}$.

Step3: Calculate $x$

$x=a + b$. Substitute the values of $a$ and $b$: $x=\frac{50\sqrt{3}}{3}+50\sqrt{3}=\frac{50\sqrt{3}+150\sqrt{3}}{3}=\frac{200\sqrt{3}}{3}\approx115.5$.

Answer:

$115.5$