SOLUTION: A scale drawing for three cities has a scale of 1cm to 10km. If A lies 75km due west of B, and c lies 50km due south of B, how far C is from A on the drawing ?

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Question 657291: A scale drawing for three cities has a scale of 1cm to 10km. If A lies 75km due west of B, and c lies 50km due south of B, how far C is from A on the drawing ?
Answer by colliefan(242) About Me  (Show Source):
You can put this solution on YOUR website!
First we will calculate the lengths in cm that the legs of the right triangle ABC have. Then, use the Pythagorean theorem to calculate the length of the hypotenuse of the right triangle which is the distance between A and C. It has to be a right triangle since since A is due west and C is due south of B.
If 1 cm = 10 km,
AB=75 km/(10 km/cm)
AB=7.5 cm*km/km
AB=7.5 cm*1
AB=7.5 cm
BC=50 km/(10 km/cm)
BC=5 cm*km/km
BC=5 cm*1
BC=5 cm

Since the legs of the triangle have lengths of 5 and 7.5 cm, the distance AC is:
a%5E2%2Bb%5E2=c%5E2
5%5E2%2B7.5%5E2=c%5E2
25%2B56.25=c%5E2
81.25=c%5E2
sqrt%2881.25%29=c
c=9.01 cm