Latoya and her dad are vacationing in New York. While taking a picture of the Statue of Liberty, she noticed her dad’s head was
directly at the top of the torch. She knew that the statue was 305 feet tall, so she wondered how far away her dad was from the base of the statue. Using the measurements below, find the distance from the base of the statue to her dad's feet. Set up a proportion, show all work.
1 answer:
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1. Check picture 1. Let the one side of the triangle be a, drop one perpendicular, CD. Then triangle ADB is a right triangle, with hypothenuse a and one side equal to 1/2a. By the Pythegorean theorem, as shown in the picture, the height is 
2. if a a=25 ft, then the height is
(ft)
3. consider picture 2. Let the length of the roof be l feet.
one side of the prism (the roof) is a rectangle with dimensions a and l, so the area of one side is a*l
the lateral Area of the roof is 3a*l
the area of the equilateral surfaces is
so the total area of the roof is
4. The total area was the 2 triangular surfaces + the 3 equal lateral rectangular surfaces. Now instead of 3 lateral triangular surfaces, we have 2.
So the total area found previously will be decreased by al
5. so the area now is
6. now a=25 and l=2a=50
Area=
=3041.3 (ft squared)
2. if a a=25 ft, then the height is
3. consider picture 2. Let the length of the roof be l feet.
one side of the prism (the roof) is a rectangle with dimensions a and l, so the area of one side is a*l
the lateral Area of the roof is 3a*l
the area of the equilateral surfaces is
so the total area of the roof is
4. The total area was the 2 triangular surfaces + the 3 equal lateral rectangular surfaces. Now instead of 3 lateral triangular surfaces, we have 2.
So the total area found previously will be decreased by al
5. so the area now is
6. now a=25 and l=2a=50
Area=
=3041.3 (ft squared)