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QuestionA building's shadow is 32 m, and the distance from the top to the shadow's tip is 35 m. Find the building's height.

Studdy Solution

STEP 1

Assumptions1. The length of the shadow of the building is32 m. . The distance from the top of the building to the tip of the shadow is35 m.
3. The problem involves a right triangle, where the height of the building, the length of the shadow, and the distance from the top of the building to the tip of the shadow are the sides of the triangle.

STEP 2

We can use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written asa2+b2=c2a^2 + b^2 = c^2where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.

STEP 3

In this problem, the distance from the top of the building to the tip of the shadow is the hypotenuse (c), the length of the shadow is one side (a), and the height of the building is the other side (b). We can write the equation asb2=c2−a2b^2 = c^2 - a^2

STEP 4

Now, plug in the given values for a and c to calculate the value of b^2.
b2=352−322b^2 =35^2 -32^2

STEP 5

Calculate the value of b^2.
b2=352−322=441b^2 =35^2 -32^2 =441

STEP 6

To find the value of b (the height of the building), we need to take the square root of b^2.
b=b2b = \sqrt{b^2}

STEP 7

Plug in the value for b^2 to calculate the value of b.
b=441b = \sqrt{441}

STEP 8

Calculate the value of b.
b=441=21b = \sqrt{441} =21The height of the building is21 m.

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