If two forces A and B pull at right angles to each other, the resultant force C can be represented by the diagonal of a rectangle. The diagonal is the hypotenuse of a right triangle. Since the opposite sides of a rectangle are equal lengths, both right triangles have the same base and height measurements, and a shared hypotenuse.
Let's consider one of the right triangles, and express the relation between the forces A, B, and C using the Pythagorean Theorem.
a^2+b^2=c^2 ⇔ A^2+B^2=C^2
We want to know if the given forces, 50 pounds and 120 pounds, will be pulled at right angles if their resultant force is 130 pounds. In order to check this, we will use the Converse of the Pythagorean Theorem.
Converse of the Pythagorean Theorem
For a triangle with sides of lengths a, b, and c, if the equation a^2+b^2=c^2 holds true, then the triangle is a right triangle with hypotenuse of length c.
Now, let's substitute A= 50, B= 120, and C= 130 into the formula and check if the equation holds true.
Since the equation holds true, the triangle formed by the forces is a right triangle. Therefore, the forces of 50 pounds and 120 pounds pull at right angles to each other.
