Russell Gossman is training for the Olympics. He wants to know the distance across Lake Royal so he can write how far he went in his training logbook each day. If from one point on the shore to one side in 13 km and from the same point to another side of the lake is 16 km. What is the approximate length in km of the lake?
This is in Pythagorean Theorem. I understand how to do it but the problem is saying that a leg is 13 km and the hypotenuse is 16 km. How to you find the length of the other leg?
Solve for b.
a^2 + b^2 = c^2
13^2 + b^2 = 16^2
169 + b^2 = 256
b^2 = 87
b = 9.33 km
All you need to do, is subtract 16^2 by 13^2 and then you get the answer. I am not going to tell you what the answer is, because I am not that nice.
To find the length of the other leg of the right triangle in this problem, you can use the Pythagorean theorem. 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 other two sides.
In this case, the hypotenuse is 16 km, and one of the legs is 13 km. Let's call the length of the other leg "x". Using the Pythagorean theorem, we can write the equation as:
x^2 + 13^2 = 16^2
Simplifying the equation, we have:
x^2 + 169 = 256
To solve for x, we can subtract 169 from both sides of the equation:
x^2 = 256 - 169
x^2 = 87
Taking the square root of both sides gives us:
x = √87
The approximate value of √87 is approximately 9.327. So, the length of the other leg (the width of the lake) is approximately 9.327 km.