Question

Finding an Unknown Side Find rounded to one decimal place.

Short answer

The value of xfrom the given triangle is 230.9

Step-by-step solution

Step 1. Given information.

The angles of a triangle are ${60}^{\circ }$,${30}^{\circ }$ .

Step 2. Formula used

The expression is framed as :$x=y+z$

Step 3. Finding the value of x

In the triangle ABD,

$\begin{array}{l}\tan 60=\frac{AD}{BD}\\ \sqrt{3}=\frac{100}{y}\\ y=\frac{100}{\sqrt{3}}\end{array}$

In triangle ABC,

$\begin{array}{c}\tan 30=\frac{AD}{DC}\\ \frac{1}{\sqrt{3}}=\frac{100}{z}\\ z=100\sqrt{3}\\ x=y+z\\ =\frac{100}{\sqrt{3}}+100\sqrt{3}\end{array}$

Now,

$\begin{array}{l}\frac{100+300}{\sqrt{3}}=\frac{400}{\sqrt{3}}\\ =230.9\end{array}$