So I’m given a triangle. The side lengths are 17, 18, and 19 is the hypotenuse. I have to find the height (x) algebraically.
How?
There is no hypotenuse, since those sides do not form a right triangle.
Still, we can get the height. If we call those sides a,b,c then using the law of cosines,
17^2 = 18^2 + 19^2 - 2*18*19*cosA
cosA = 11/19
So, the height h (from C to AB), is given by
h/18 = sinA
h = 18 sinA = 18√(1 - (11/19)^2) = 72/19 √15
If you wanted the height to some other side, you'll have to go through these steps with the appropriate modifications.
To find the height (x) of a triangle with side lengths 17, 18, and 19, we can use algebraic methods. Here's how:
Step 1: Start by labeling the triangle. Let's call the side lengths a = 17, b = 18, and c = 19 (where c is the hypotenuse).
Step 2: Use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b):
c^2 = a^2 + b^2
In this case, 19^2 = 17^2 + 18^2.
Step 3: Simplify the equation:
361 = 289 + 324
Step 4: Combine like terms:
361 = 613
However, since 361 ≠ 613, there must be an error in the calculation. Please check the given side lengths and ensure they are accurate.