David wants to find the height of a building. He places his 5050 feet ladder against the very top of the building. David then measures the base of the building to his ladder which is 1010 feet. How tall is the building? Round your answer to the nearest tenth.
Using the information given, we can form a right triangle with the ladder as the hypotenuse, the height of the building as one leg, and the distance from the base of the building to the ladder as the other leg.
Let x be the height of the building. Applying the Pythagorean theorem, we have:
x^2 + 10^2 = 50^2
x^2 + 100 = 2500
x^2 = 2400
x = √2400
x ≈ 49 feet
Therefore, the height of the building is approximately 49 feet tall.