1. ## geometry angle problem

A road 12m wide runs through a tunnel 18m high.the cross section is a major segment of a circle seen below(excuse my drawing lol)
i)calculate the radius, BC, of the cirlce
ii)find the angle ABC
iii)find the cross sectioanl area of the tunnel

2. Is this what you mean?. You know, you can make circles with paint.

If so, you can find the radius by using $r^{2}-(18-r)^{2}=36$

We find that r=10.

Now that we have r, the rest is easier.

The angle can be found by using the formula for a long chord, $12=2rsin(\frac{\theta}{2})$

Since r=10, we have $12=20sin(\frac{\theta}{2})$, Solve for theta and we get ${\theta}=2sin^{-1}(\frac{3}{5})$

Then, after you have theta, you can use the formula for the area of a segment of a circle to find its area.

That formula is $\frac{1}{2}r^{2}{\theta}$

3. thank u