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PSYCHO15rus [73]
3 years ago
13

Please help!! Everything is in the photo

Mathematics
1 answer:
Nutka1998 [239]3 years ago
8 0
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.
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