Geometry measurements?

Question

A young man is 36 meters away from a building and looking at a bird sitting on top of the building. The man knows he is 85 meters away from the bird. How tall is the building?

 

the building is __ tall? 

 

Please explain

 

thanks

Answer 1

This is is a Pythagorean theorem problem. For this you need a right angle triangle. 

 

So you draw the ground, on one end is the building and on the other end is the man. That is the base of the triangle and it is 36m. The building is the height of the triangle. Last, you draw a straight line from the man to the top of the building where the bird is which is 85m. (This line is also your hypotenuse) 

 

Since the building is a tall straight line on the ground (base), these two lines make a 90 degree angle. Which is why you have a right triangle. 

 

The Pythagorean theorem states:

 

base^2 + height^2 = hypotenuse^2. 

 

For this question, you need to find the height. So you'll re-write the equation: 

 

height^2 = hypotenuse^2 - base^2

height^2 = 85^2 - 36^2

height^2 = 5929 

 

To find the height, you have to take the square root of height^2 and 5929. 

 

So, height = 77 meters