3 years ago

Help please me with this ....

Mathematics

1 answer:

Nonamiya [84]3 years ago

5 0

Ext. 13/44 hope it helpa

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Kathy lives directly east of the park. The football field is directly south of the park. The library sits on the line formed bet

enyata [817]

Look at the picture in the attachment.

Using the Pythagorean theorem, set up a system of three equations:
$x^2+y^2=(12+9)^2 \\
12^2+z^2=x^2 \\
9^2+z^2=y^2 \\ \\
x^2+y^2=441 \\
144+z^2=x^2 \\
81+z^2=y^2$

$\hbox{substitute } 144+z^2 \hbox{ for } x^2 \hbox{ and } 81+z^2 \hbox{ for } y^2 \hbox{ in the first equation:} \\
144+z^2+81+z^2=441 \\
225+2z^2=441 \\
2z^2=441-225 \\
2z^2=216 \\
z^2=\frac{216}{2} \\
z^2=108 \\
z=\sqrt{108} \\
z=\sqrt{36 \times 3} \\
z=6\sqrt{3} \\ z \approx 10.39$

$81+z^2=y^2 \\
81+108=y^2 \\
189=y^2 \\
\sqrt{189}=y \\
\sqrt{9 \times 21}=y \\
y=3\sqrt{21} \\ y \approx 13.75$

a. The library is approximately 10.39 miles (exactly: 6√3 miles) from the park.
b. The park is approximately 13.75 miles (exactly: 3√21 miles) from the football field.