Answer:
Part 1) ![c=\sqrt{146}\ cm](https://tex.z-dn.net/?f=c%3D%5Csqrt%7B146%7D%5C%20cm)
Part 2) ![c=8\sqrt{2}\ in](https://tex.z-dn.net/?f=c%3D8%5Csqrt%7B2%7D%5C%20in)
Part 3) The diagonal of rectangle is ![d=3\sqrt{29}\ cm](https://tex.z-dn.net/?f=d%3D3%5Csqrt%7B29%7D%5C%20cm)
Part 4) The length of the diagonal of computer monitor is ![d=15\ in](https://tex.z-dn.net/?f=d%3D15%5C%20in)
Part 5) The ramp is
long
Part 6) The distance between their houses is ![=4\sqrt{2}\ mi](https://tex.z-dn.net/?f=%3D4%5Csqrt%7B2%7D%5C%20mi)
Part 7) ![234.31\ mi](https://tex.z-dn.net/?f=234.31%5C%20mi)
Part 8) 120 feet of wire is required
Step-by-step explanation:
Part 1) we know that
To find the length of the hypotenuse in a right triangle apply the Pythagorean Theorem
![c^2=a^2+b^2](https://tex.z-dn.net/?f=c%5E2%3Da%5E2%2Bb%5E2)
where
c is the hypotenuse (the greater side)
a and b are the legs
we have
![a=11\ cm\\b=5\ cm](https://tex.z-dn.net/?f=a%3D11%5C%20cm%5C%5Cb%3D5%5C%20cm)
substitute
![c^2=11^2+5^2](https://tex.z-dn.net/?f=c%5E2%3D11%5E2%2B5%5E2)
![c^2=146](https://tex.z-dn.net/?f=c%5E2%3D146)
![c=\sqrt{146}\ cm](https://tex.z-dn.net/?f=c%3D%5Csqrt%7B146%7D%5C%20cm)
Part 2) we know that
To find the length of the hypotenuse in a right triangle apply the Pythagorean Theorem
![c^2=a^2+b^2](https://tex.z-dn.net/?f=c%5E2%3Da%5E2%2Bb%5E2)
where
c is the hypotenuse (the greater side)
a and b are the legs
we have
![a=8\ in\\b=8\ in](https://tex.z-dn.net/?f=a%3D8%5C%20in%5C%5Cb%3D8%5C%20in)
substitute
![c^2=8^2+8^2](https://tex.z-dn.net/?f=c%5E2%3D8%5E2%2B8%5E2)
![c^2=128](https://tex.z-dn.net/?f=c%5E2%3D128)
![c=\sqrt{128}\ in](https://tex.z-dn.net/?f=c%3D%5Csqrt%7B128%7D%5C%20in)
simplify
![c=8\sqrt{2}\ in](https://tex.z-dn.net/?f=c%3D8%5Csqrt%7B2%7D%5C%20in)
Part 3) we know that
To find the length of the diagonal in a rectangle apply the Pythagorean Theorem
![d^2=b^2+h^2](https://tex.z-dn.net/?f=d%5E2%3Db%5E2%2Bh%5E2)
where
d is the diagonal of rectangle
b and h are the base and the height of rectangle
we have
![b=15\ cm\\hb=6\ cm](https://tex.z-dn.net/?f=b%3D15%5C%20cm%5C%5Chb%3D6%5C%20cm)
substitute
![d^2=15^2+6^2](https://tex.z-dn.net/?f=d%5E2%3D15%5E2%2B6%5E2)
![d^2=261](https://tex.z-dn.net/?f=d%5E2%3D261)
![d=\sqrt{261}\ cm](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B261%7D%5C%20cm)
simplify
![d=3\sqrt{29}\ cm](https://tex.z-dn.net/?f=d%3D3%5Csqrt%7B29%7D%5C%20cm)
Part 4) we know that
To find the length of the diagonal of a computer monitor apply the Pythagorean Theorem
![d^2=w^2+h^2](https://tex.z-dn.net/?f=d%5E2%3Dw%5E2%2Bh%5E2)
where
d is the diagonal of computer monitor
w and h are the wide and the high of computer monitor
we have
![w=12\ in\\h=9\ in](https://tex.z-dn.net/?f=w%3D12%5C%20in%5C%5Ch%3D9%5C%20in)
substitute
![d^2=12^2+9^2](https://tex.z-dn.net/?f=d%5E2%3D12%5E2%2B9%5E2)
![d^2=225](https://tex.z-dn.net/?f=d%5E2%3D225)
![d=\sqrt{225}\ in](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B225%7D%5C%20in)
simplify
![d=15\ in](https://tex.z-dn.net/?f=d%3D15%5C%20in)
Part 5) we know that
To find out the length of the ramp apply the Pythagorean Theorem
![L^2=x^2+y^2](https://tex.z-dn.net/?f=L%5E2%3Dx%5E2%2By%5E2)
where
L is the length of the ramp
x is the horizontal distance of the ramp
y is the vertical distance of the ramp
we have
![x=10\ ft\\y=3.5\ ft](https://tex.z-dn.net/?f=x%3D10%5C%20ft%5C%5Cy%3D3.5%5C%20ft)
substitute
![L^2=10^2+3.5y^2](https://tex.z-dn.net/?f=L%5E2%3D10%5E2%2B3.5y%5E2)
![L^2=112.25](https://tex.z-dn.net/?f=L%5E2%3D112.25)
![L=10.59\ ft](https://tex.z-dn.net/?f=L%3D10.59%5C%20ft)
Part 6) we know that
To find the distance between their houses apply the Pythagorean Theorem
![c^2=a^2+b^2](https://tex.z-dn.net/?f=c%5E2%3Da%5E2%2Bb%5E2)
where
c is the hypotenuse (distance between their houses)
a and b are the legs
we have
![a=4\ mi\\b=4\ mi](https://tex.z-dn.net/?f=a%3D4%5C%20mi%5C%5Cb%3D4%5C%20mi)
substitute
![c^2=4^2+4^2](https://tex.z-dn.net/?f=c%5E2%3D4%5E2%2B4%5E2)
![c^2=32](https://tex.z-dn.net/?f=c%5E2%3D32)
![c=4\sqrt{2}\ mi](https://tex.z-dn.net/?f=c%3D4%5Csqrt%7B2%7D%5C%20mi)
Part 7) we know that
The speed is equal to divide the distance by the time
![speed=distance/time](https://tex.z-dn.net/?f=speed%3Ddistance%2Ftime)
so
the distance is equal to multiply the speed by the time
![distance=speed*time](https://tex.z-dn.net/?f=distance%3Dspeed%2Atime)
<em>First train</em>
speed=60 mph
time=3 hours
distance=60(3)=180 miles
<em>Second train</em>
speed=50 mph
time=3 hours
distance=50(3)=150 miles
To find out how far apart are the trains at the end of 3 hours apply the Pythagorean Theorem
![c^2=a^2+b^2](https://tex.z-dn.net/?f=c%5E2%3Da%5E2%2Bb%5E2)
where
c is the hypotenuse (distance between the trains)
a and b are the legs
we have
![a=180\ mi\\b=150\ mi](https://tex.z-dn.net/?f=a%3D180%5C%20mi%5C%5Cb%3D150%5C%20mi)
substitute
![c^2=180^2+150^2](https://tex.z-dn.net/?f=c%5E2%3D180%5E2%2B150%5E2)
![c^2=54,900](https://tex.z-dn.net/?f=c%5E2%3D54%2C900)
![c=234.31\ mi](https://tex.z-dn.net/?f=c%3D234.31%5C%20mi)
Part 8) we know that
For one tree is needed three wire
To find out the length of one wire apply the Pythagorean Theorem
![c^2=a^2+b^2](https://tex.z-dn.net/?f=c%5E2%3Da%5E2%2Bb%5E2)
where
c is the hypotenuse (length of one wire)
a and b are the distance above the ground and the distance from the base
we have
![a=3\ ft\\b=4\ ft](https://tex.z-dn.net/?f=a%3D3%5C%20ft%5C%5Cb%3D4%5C%20ft)
substitute
![c^2=3^2+4^2](https://tex.z-dn.net/?f=c%5E2%3D3%5E2%2B4%5E2)
![c^2=25](https://tex.z-dn.net/?f=c%5E2%3D25)
![c=5\ ft](https://tex.z-dn.net/?f=c%3D5%5C%20ft)
so
For one tree is required ----> (5)3=15 ft
therefore
For 8 trees is required
Multiply by 8
15(8)=120 ft