Josephine was asked to make a one-fiftieth scale model of the new water tower for her town. She constructed the model that is sh
own below. What is the height of the town’s new water tower in feet? Round to the nearest whole number. 22 feet 40 feet 63 feet 113 feet
2 answers:
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Answer:
s = 16.97 units
Step-by-step explanation:
Since this is a right triangle, we can use trigonometry to figure out the lengths of the sides.
Look at the 45 degree angle. We can use the opposite side (12) and the hypotenuse (s) to solve for s.
Opposite and hypotenuse is sine, so we are using sine. The sine of 45 degrees is 0.70710678118. Make an equation like so:
- 0.70710678118 =
, and we are solving for s.
Put a 1 in the denominator of sine(45 degrees) so you can cross-multiply.
Cross multiply.
- 0.70710678118s = 12
Divide both sides by sine(45 degrees).
- s = 16.97
The length of side s is 16.97 units.
Another way to have done this problem is to use the Pythagorean theorem: a^2 + b^2 = c^2
Substitute 12 for a and b and solve for c, the hypotenuse.
- (12)^2 + (12)^2 = c^2
Evaluate the exponents.
- 144 + 144 = c^2
Add them together.
- 288 = c^2
Square root 288 to solve for c.
c = 16.97, which is the same answer as you got using trigonometry.