Hello!
The pythagorean theorem states that a² + b² = c² in a right triangle. In this theorem, a and b are legs (shorter sides) and c is the hypotenuse, which is the longest side and diagonal from the 90 degree angle.
1. How high is the flag pole?
In this question, they have given you the values of a and c. From the figure, a is equal to 100 feet, and the longest side is equal to 125 feet. With those values, we can find the height of the flag pole, or the other leg, b, but in the given diagram, they use x.
100² + x² = 125² (simplify)
10000 + x² = 15625 (subtract both sides by 10000)
5625 = b² (take the square root of both sides)
x = 75
Therefore, the height of the flag pole is 75 feet long.
2. How long is the longest side of the sail?
The longest side of every right triangle is the hypotenuse or c, but in this diagram, they use x. The value of leg a is 3 meters, and the value of leg b is 5 meters. With those values, we can find the length of the longest side of the sail.
3² + 5² = x² (simplify)
9 + 25 = x² (add)
36 = x² (take the square root of both sides)
x = 6
Therefore, the longest side of the sail is 6 meters long.
Answers:
1. 75 feet
2. 6 meters