To solve this problem, use the Pythagorean Theorem to find the third side.


7 is the hypotenuse

third side= sqart(7^2-5^2)

I thought the Pythagorean Theorem was a^2+b^2=c^2? Where did the "-" come from in 7^2-5^2?

To solve this problem, you need to use the trigonometric function known as cosine (cos) and the information given, which is cos = 5/7.

The Pythagorean Theorem is not directly applicable here since it relates to right triangles, and the cosine function involves all types of triangles.

Now, to find the third side, we first need to understand the relationship between cosine, adjacent side, and hypotenuse in a right triangle. In a right triangle, the adjacent side is the side adjacent (next to) the given angle, and the hypotenuse is the longest side, opposite the right angle.

The cosine of an angle (in this case, which is not clear), is defined as the ratio of the adjacent side length to the hypotenuse length.

Let's assume the angle we are considering is θ. We have: cos(θ) = adjacent side / hypotenuse.

From the given information, we know that cos(θ) = 5/7.

To find the third side, we need more information, such as the length of one of the sides (adjacent or hypotenuse) or the measure of one of the other angles. With only the cosine, it is not possible to determine the exact lengths of the adjacent side or hypotenuse, and consequently, we cannot find the third side.

So, in this case, with only the information that cos = 5/7, we can't determine the length of the third side.