what is the hypotenuse of a right angle triangle where the 2 sides are 15/16 and 15/16
+9466 The two legs must be 15/16 and 15/16 .
We can use the Pythagorean theorem to find the hypotenuse, which says....
(hypotenuse)2 = (leg)2 + (other leg)2
Plug in 15/16 for the legs.
(hypotenuse)2 = (15/16)2 + (15/16)2
Multiply out the exponents.
(hypotenuse)2 = 225 / 256 + 225/256
Add the fractions.
(hypotenuse)2 = 450 / 256
Take the positive square root of both sides.
hypotenuse = √( 450 / 256 )
hypotenuse = √450 / √256
hypotenuse = 15√2 / 16 ≈ 1.326
+2441 We could make this problem easier computationally once we realize that this triangle must be an isosceles right triangle. An isosceles triangle happens to be a 45-45-90 triangle, a triangle that happens to be apart of the "special right triangles" category.
In a 45-45-90 triangle, know the ratio of the side lengths are \(1:1:\sqrt{2}\). Now, let's solve for the hypotenuse.
| \(\frac{\frac{15}{16}}{1}=\frac{\text{hypotenuse}}{\sqrt{2}}\) | multiply by the square root of 2 on both sides. |
| \(\frac{15}{16}\sqrt{2}=\text{hypotenuse}\) | |
As you'll notice, this is the exact answer that hecticar got. I ust used a different method.
