Question 845041:
Answer by pmesler(52)   (Show Source):
You can put this solution on YOUR website! The length of a shadow of a building is 8ft. The distance from the top of the building to the tip of the shadow is 14 ft. Find the height of the building. Round your answer to the nearest tenth
It always helps to draw a picture. Since I can't do that here, try and visualize and draw my explanation.
We know that a building stands perpendicular to the ground and forms a 90 degree angle. Therefore we are dealing with a right triangle.
From the information provided, we can say that the length of the building forms one side of a right triangle and we will label that as a. We don't know what a is, but we know what b and c is. That's all we need to know. Here's why:
We know the shadow is 8ft long. Shadows form horizontally and is therefore the bottom leg of the right triangle and we will call this length b. b = 8 ft. Next, we read that the distance from the top of the building to the tip of the shadow is 14 ft. This length is the hypotenuse and is the longest leg of the right triangle. We will call that side c and c = 14 ft.
Now we simply apply the Pythagorean Theorem which states that a^2 + b^2 = c^2.
Let's substitute into the equation what we do know. We know that b = 8 ft, and c = 14 ft, but we don't know what a is, so we write the equation as such:
a^2 + 8^2 = 14^2
that gives us
a^2 + 64 = 196
Now let's solve for a. The first thing we need to do is isolate a to the left side of the equation. We do this by subtracting 64 from both sides to obtain the following:
a^2= 196 - 64
a^2 = 132. We're not done yet. We need to get rid of the squaring function. To "undo" the squaring function we need to perform the inverse function, in this case take the square root of both sides of the equation so all we are left with on the left side is a and on the right the square root of 132.
sqrt(a^2) = sqrt(132).
a = sqrt(132)
a = 11.489 or approximately 11.5 ft. Therefore the height of the building is 11.5 ft.
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