Very true !phinds said:DRAW THE DAMN PICTURE. All of the other suggestions here are good but if you don't start off by drawing a reasonable picture of what you're working with, you're shooting in the dark.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. To find the height of a triangle, you can use this formula: h = √(a^2 - b^2), where h is the height, a and b are the lengths of the other two sides, and √ represents the square root.
For an equilateral triangle, where all three sides are equal, the height can be found using the formula h = (√3/2) x s, where h is the height and s is the length of any side. This formula is derived from splitting the equilateral triangle into two right triangles, where the height is the longer side of the triangle.
Yes, the formula for finding the height of any triangle when the area and base are known is h = (2 x A)/b, where h is the height, A is the area, and b is the base. This formula is derived from the area of a triangle formula, where A = (1/2) x b x h. By rearranging the formula, we can solve for h.
Trigonometry can be used to find the height of a triangle if you know one angle and one side length. You can use the trigonometric function tangent (tan) to find the height. The formula is h = b x tan(θ), where h is the height, b is the length of the adjacent side, and θ is the angle between the adjacent side and the hypotenuse. This method is particularly useful for finding the height of a triangle on a coordinate plane.
Yes, there is a shortcut called the "altitude-on-hypotenuse" theorem. This theorem states that the length of the altitude (height) to the hypotenuse of a right triangle is equal to the geometric mean of the segments of the hypotenuse. In other words, if the hypotenuse has lengths a and b, and the altitude has length h, then h = √(ab). This method can save time and effort when finding the height of a right triangle.