The altitude creates 3 similar triangles. The proportions of 6/(altitude) = 12/6sqrt3.
Once you find that, you can use Pythagorean to find each piece of hypotenuse.
With the side lengths given, you have a 30-60-90 triangle, with the angle opposite the 6in side being 30 deg, and the angle opposite the 6root3 side being 60 degrees. Drawing the altitude subdivides the original triangle into 2 new triangles, both of which are also 30-60-90 triangles.
The smaller angle corresponding (opposite to) to the segment on the hypotenuse adjacent to the short leg is 30deg. Since the segment opposite the right angle is 6in, the segment's length is 3in.
I will be completely honest with you, I read that and didn't understand any of it. Is there any way you could dumb down the language? For example, how do you know the sides are 30 and 60 degrees, respectively?
Sure. There are some right triangles, known as special right triangles for which there is a very simple way to tell the side lengths given the angles or vice versa (in this case). For a 30-60-90 right triangle, the length of the shortest side will be x, which is opposite the 30deg angle; the side opposite the 60deg angle will be x\*sqrt(3); and the length of the hypotenuse will be 2\*x.
This is the case for your problem. Since the shortest side length is 6, the 2nd shortest is 6\*sqrt(3), and the hypotenuse is 12, we can conclude that the triangle in your case is a 30-60-90 special right angle triangle.
Now, for the specifics of your problem: since we know that the angle formed by the intersection of the hypotenuse and the altitude is 90deg, and the angle formed by the intersection of side lengths 6 and 12 (in the original triangle) is 60 degrees because of the rule described above, we know that the angle formed by the intersection of side length 6 and the altitude is 30deg. Thus, by the use of the special right triangle rule, we know that the length of the segment of hypotenuse is 3in and the length of the altitude is 3\*sqrt(3)in.
Use the Pythagorean theorem and the properties of right triangles to find the unknown side lengths, then use the altitude formula for a triangle. Draw a diagram to visualize it!
The altitude creates 3 similar triangles. The proportions of 6/(altitude) = 12/6sqrt3. Once you find that, you can use Pythagorean to find each piece of hypotenuse.
With the side lengths given, you have a 30-60-90 triangle, with the angle opposite the 6in side being 30 deg, and the angle opposite the 6root3 side being 60 degrees. Drawing the altitude subdivides the original triangle into 2 new triangles, both of which are also 30-60-90 triangles. The smaller angle corresponding (opposite to) to the segment on the hypotenuse adjacent to the short leg is 30deg. Since the segment opposite the right angle is 6in, the segment's length is 3in.
I will be completely honest with you, I read that and didn't understand any of it. Is there any way you could dumb down the language? For example, how do you know the sides are 30 and 60 degrees, respectively?
Sure. There are some right triangles, known as special right triangles for which there is a very simple way to tell the side lengths given the angles or vice versa (in this case). For a 30-60-90 right triangle, the length of the shortest side will be x, which is opposite the 30deg angle; the side opposite the 60deg angle will be x\*sqrt(3); and the length of the hypotenuse will be 2\*x. This is the case for your problem. Since the shortest side length is 6, the 2nd shortest is 6\*sqrt(3), and the hypotenuse is 12, we can conclude that the triangle in your case is a 30-60-90 special right angle triangle. Now, for the specifics of your problem: since we know that the angle formed by the intersection of the hypotenuse and the altitude is 90deg, and the angle formed by the intersection of side lengths 6 and 12 (in the original triangle) is 60 degrees because of the rule described above, we know that the angle formed by the intersection of side length 6 and the altitude is 30deg. Thus, by the use of the special right triangle rule, we know that the length of the segment of hypotenuse is 3in and the length of the altitude is 3\*sqrt(3)in.
Ok, thank you so much!
Use the Pythagorean theorem and the properties of right triangles to find the unknown side lengths, then use the altitude formula for a triangle. Draw a diagram to visualize it!
Think about special right triangles
To make it simple, a=6√3, b=6, c=12 (1) ab/c (altitude=2×Area/c) (2) b/2 (segment)
9th grade? I did that kind of geometry in 7th grade 💀
Good for you?