You want the formula to find the height of the triangle as you have the length of the hypotoneous?

Answer 1

I'm assuming this is aright triangle, since the word "hypotenuse" has no meaning for non-right triangles. The word "height" is ambiguous here, without knowing the orientation of the triangle. Is the hypotenuse horizontal? Is it diagonal, with one of the sides horizontal and the other vertical? That's the normal way that right triangles are drawn, so I'll assume that's what you're talking about. The formula you need is the Pythagorean theorum, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the two other sides. The hypotenuse is the side that is opposite the right angle. The other two sides are "adjacent" to the right angle. If you let c = the length of the hypotenuse, and a and b equal the lengths of the two adjacent sides, the Pythagorean theorum can be expressed as: a2 + b2 = c2 But, you don't have enough information to solve this formula. Assuming the triangle is oriented with one adjacent side horizontal and the other adjacent side vertical, let's say that a is the length of the vertical side and b is the length of the horizontal side (you could do it the other way, and the formula is still valid, but it just makes the following discussion easier for me to assume one or the other, so I pick a to be the vertical side). you want to solve for either a. You have the value of c (the length of the hypotenuse. But that's not enough. You also need the value of b. You see, the equation for the Pythagorean theorum can be re-arranged as: a2 = c2 - b2 then a2 = √(c2 - b2) But this equation is not solvable for a because you do not know the value of b. If you find the length of b, in addition to the length of c, you can solve for a. Til then, this equation will not help you. Note that, if your triangle is not oriented as I have assumed, this formula won't work anyway. If your hypotenuse is horizontal, then the "height" of your triangle will not be the length of either side, but the length of a line drawn from the right angle (at the top of the triangle) straight down to the hypotenuse, intersecting it perpendicularly. Now, you have to figure out the length of this new line, which is actually one of the adjacent sides of both of the two new right triangles created by the addition of this line. You can still use the Pythagorean theorum, but now you don't know a, b, OR c. And you can't figure them out, without knowing the measurements of at least one of the two non-right angles. And even if you had the angle measurement, the formula still won't work by itself - you will need to use trigonometric functions to find the lengths of the sides of the three triangles.