Question

Determine the value of x. Round to the nearest foot.

Answer 1

Given:

Given that a cross section of gazebo.

Required:

To find the value of x.

Explanation:

From the given figure the left side triangle is a right triangle.

And having side value,

$\begin{gathered} c=22-2 \\ \\ =20feet \end{gathered}$

And angle,

$\begin{gathered} \angle A=10 \\ \angle C=90 \end{gathered}$

Now we have to find the other two side values.

Now we find the height of the triangle let it be 'a'.

Now by using sine rule,

$\begin{gathered} \frac{\sin A}{a}=\frac{\sin C}{c} \\ \\ \frac{\sin10}{a}=\frac{\sin90}{20} \\ \\ \frac{0.1736}{a}=\frac{1}{20} \\ \\ a=3.4729 \end{gathered}$

Now we have to find the value of other side let the other side be 'b',

Now

$\begin{gathered} c^2=a^2+b^2 \\ \\ 20^2=(3.4729)^2+b^2 \\ \\ b^2=400-12.061 \\ \\ b^2=387.939 \\ \\ b=19.6961 \end{gathered}$

Now the value of x is,

$\begin{gathered} x=2b \\ \\ x=2(19.6961) \\ \\ x=39.39 \\ \\ x\approx39feet \end{gathered}$

Final Answer:

$x=39feet$