SOLUTION: Use a proportion to set up and solve the following problem. Round your answer to the nearest tenth if necessary. If a 7.5 ft tall petrified stump casts a 12 ft long shadow, the

Question 995749: Use a proportion to set up and solve the following problem. Round your answer to the nearest tenth if necessary.
If a 7.5 ft tall petrified stump casts a 12 ft long shadow, then how tall is a statue that casts a 17.9 ft shadow?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
7.5 / 12 = x / 17.9

cross multiply to get 7.5 * 17.9 = 12 * x

simplify to get 134.25 = 12x

solve for x to get x = 134.25/12 = 11.1875.

the assumption is that the rays of the sun are coming in at the same relative to the ground.

if 7.5 is the vertical and 12 is the horizontal, then the angle from the ground to the sun is tan(7.5/12)

similarly, if 11.1875 is the vertical and 17.9 is the horizontal, then the angle from the ground to the sun is tan(11.1875/17.9)

tan(7.5/12) is equal to tan(.625)

tan(11.1875/17.9) is equal to tan(.625)

if the tangent function is the same, then the angles are the same if they are in the same quadrant, or they have the same reference angle if they are in different quadrants.

that's trigonometry.

if you haven't had it, then assume both angles are in the same quadrant, so they have to be the same.

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