Question

Please help!! Everything is in the photo

Answer 1

A) Pine Road and Oak Street form a right angle, so we can extract the relation

$\tan30^\circ=\dfrac x{11\sqrt3}\implies\dfrac1{\sqrt3}=\dfrac x{11\sqrt3}\implies x=11$

where $x$ is the distance we want to find (bottom side of the rectangle).

Alternatively, we can use the other given angle by solving for $x$ in

$\tan60^\circ=\dfrac{11\sqrt3}x$

but we'll find the same solution either way.

b) Pine Road and Oak Street form a right triangle, with Main Street as its hypotenuse. We can use the Pythagorean theorem to find how long it is.

$(\text{Pine})^2+(\text{Oak})^2=(\text{Main})^2$

Let $y$ be the length of Main Street. Then

$(11\sqrt3)^2+11^2=x^2\implies x^2=484\implies x=\pm22$

but of course the distance has to be positive, so $x=22$.