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Show us what you're doing. Where did you get one side being 4 in length?cupcakes said:Homework Statement
Please see picture attached.
Homework Equations
The Attempt at a Solution
If I use the pythagoras formula with the ratio I get the height as 3 yet it is longer than the side that is 4. Am I doing something wrong? Thanks.
Mark44 said:Show us what you're doing. Where did you get one side being 4 in length?
That reasoning is flawed. It's given that the ratio of BC to AC is 5/8, but that doesn't mean that BC is 5 and AC is 8. For example, BC could be 1, and AC could be 1.6, or BC could be 2, with AC being 3.2. There are literally an infinite number of pairs of values of BC and AC that would give this ratio; you can't get the lengths from the ratio.Acala said:He is saying that he halved line AC in order to get a half-length of 4
Acala said:, and he used the Pythagorean theorem with side AB (or BC) in order to get length BD in terms of the other sides' lengths.
The problem is that the illustration is not drawn to scale. Side BC should be shorter than AC, as can be seen by the ratio. What to do next, I don't know.
Mark44 said:That reasoning is flawed. It's given that the ratio of BC to AC is 5/8, but that doesn't mean that BC is 5 and AC is 8. For example, BC could be 1, and AC could be 1.6, or BC could be 2, with AC being 3.2. There are literally an infinite number of pairs of values of BC and AC that would give this ratio; you can't get the lengths from the ratio.
The Pythagoras formula for finding the height of a triangle is h = √(a² - b²), where h is the height, a is the length of the base, and b is the length of the perpendicular side.
Yes, the Pythagoras formula can be applied to any type of triangle, whether it is a right triangle, acute triangle, or obtuse triangle.
The base of a triangle is typically the longest side and it is opposite the largest angle. The perpendicular side is the side that forms a right angle with the base.
Yes, you can use the Pythagoras formula to find the height of a triangle if you know the lengths of two sides. You can use the formula h = √(a² - b²), where h is the height, a is one of the known sides, and b is the other known side.
Yes, there are alternative methods for finding the height of a triangle, such as using trigonometric ratios or the area formula (h = 2A/b, where A is the area and b is the length of the base). However, the Pythagoras formula is often the simplest and most straightforward method.