1. Find the height from the known area and base length.
Think back to the area formula of a triangle. The area formula of triangle is A= 1/2bh.
A = area of triangle
B = the length of the base of the triangle
H = the height of the base of the triangle
Look at your triangle and determine which variables are known. In this example, you already know the area, so you can substitute the area value into a in the formula. You also know the size of the base length, so you can substitute the value into the "b" in the formula. If you don't know the area or length of the bottom, then you can only try other methods.
No matter how the triangle is drawn, any side of the triangle can be used as the bottom. In order to show it more vividly, you can imagine rotating the triangle until the side length is known at the bottom.
For example, given that the area of a triangle is 20 and the length of one side is 4, A = 20 and b = 4 are brought in.
Substitute the numerical value into the formula A= 1/2bh, and then calculate. First multiply the base length (b) by 1/2, and then divide it by the area (a). The result of the operation should be the height of the triangle!
In this example: 20 =1/2 (4) h.
20 = 2h
10 = h
2. Find the height of an equilateral triangle
Recall the characteristics of equilateral triangles. An equilateral triangle has three equal sides, and each side has an included angle of 60 degrees. If you divide an equilateral triangle into two halves, you will get two identical right triangles.
In this example, we use an equilateral triangle with a side length of 8.
Recall Pythagorean Theorem. Pythagorean theorem describes two right-angled sides as A and B, and the hypotenuse as C: A2+B2 = C2. We can use this theorem to find the height of an equilateral triangle!
Cut the equilateral triangle in half, substitute the values into variables A, B, C, and the hypotenuse C is equal to the original hypotenuse length. The length of the right-angled side A becomes 1/2 of the side length, and the right-angled side B is the height of the triangle.
Take an equilateral triangle of length 8 as an example, where c = 8 and a = 4.
Substitute the numerical value into Pythagorean theorem formula to find b2. Multiply the side length c and a to get the square value. Then subtract a2 from c2.
42 + b2 = 82
16 + b2 = 64
b2 = 48
Find the root of b2 and get the height of the triangle! Sqrt(2) is calculated by using the root number of the computer. The result is the height of an equilateral triangle!
b = Sqrt (48) = 6.93
3. Find the height of the known side length and angle
Identify the variables you know. If you know an included angle and a side length of a triangle, if this angle is the included angle between the bottom and the known side, or if the three side lengths are known, you can find the height of the triangle. We call the three sides of a triangle A, B and C, and the triangle A, B and C. ..
If you know the length of three sides of a triangle, you can find the height of the triangle with sea formula.
If the length of two sides and an angle are known, it can be solved by the area formula A = 1/2ab(sin C).
If you know the length of three sides, you can also use the form of sea. Ocean style is divided into two parts. First, you must solve the variable S, which is equal to half the circumference of a triangle. You can use this formula: s = (a+b+c)/2.
For example, if the three sides of a triangle are a = 4, b = 3 and c = 5, then s = (4+3+5)/2, which means s = (12)/2. Find s = 6.
Then use the second part of the sea. Area = sqr(s(s-a)(s-b)(s-c)。 Then substitute the area into the formula of high area: 1/2bh (or 1/2ah, 1/2ch).
Calculate the height. In this example, it is1/2 (3) h = sqr (6 (6-4) (6-3) (6-5). Simplified as 3/2h = sqr(6(2)(3)( 1), that is, 3/2h = sqr(36). Calculate the square root with a calculator and get 3/2h = 6. Therefore, based on the side length b, the height of the triangle is greater than 4.
If the length of an edge and an included angle are known, use the area formula of two edges and an angle to solve it. The triangle area formula 1/2bh is used to replace the area in the above formula. The formula becomes 1/2bh = 1/2ab(sin C) and is simplified to get h = a(sin C), so that a variable with unknown side length can be eliminated.
Solve equations according to known variables. For example, given a = 3 and C = 40 degrees, you can get "h = 3(sin 40)" by substituting it into the formula. Calculate the equation with a calculator, and the height h is approximately equal to 1.928.