How is the height of the triangle found. Find the greatest height of the triangle. Protection of personal information
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First of all, a triangle is a geometric figure that is formed by three points that do not lie on one straight line, which are connected by three segments. To find what the height of a triangle is, you must first determine its type. Triangles differ in the size of the angles and the number of equal angles. In terms of angles, a triangle can be acute-angled, obtuse-angled and rectangular. By the number of equal sides, isosceles, equilateral and versatile triangles are distinguished. Height is the perpendicular that is dropped to the opposite side of the triangle from its apex. How do I find the height of a triangle?
How to find the height of an isosceles triangle
An isosceles triangle is characterized by the equality of the sides and angles at its base, therefore, the heights of an isosceles triangle drawn to the lateral sides are always equal to each other. Also, the height of this triangle is both the median and the bisector. Accordingly, the height divides the base in half. Consider the resulting right-angled triangle and find the side, that is, the height of the isosceles triangle, using the Pythagorean theorem. Using the following formula, we calculate the height: H = 1/2 * √4 * a 2 - b 2, where: a is the side of this isosceles triangle, b is the base of this isosceles triangle.
How to find the height of an equilateral triangle
A triangle with equal sides is called equilateral. The height of such a triangle is derived from the formula for the height of an isosceles triangle. It turns out: H = √3 / 2 * a, where a is the side of this equilateral triangle.
How to find the height of a versatile triangle
A multi-sided triangle is a triangle in which any two sides are not equal to each other. In such a triangle, all three heights will be different. You can calculate the lengths of heights using the formula: H = sin60 * a = a * (sgrt3) / 2, where a is the side of the triangle, or first calculate the area of a particular triangle using Heron's formula, which looks like: S = (p * (pc) * (pb) * (pa)) ^ 1/2, where a, b, c are the sides of a versatile triangle, and p is its semiperimeter. Each Height = 2 * Square / Side
How to find the height of a right triangle
A right-angled triangle has one right angle. The height that goes to one of the legs is at the same time the second leg. Therefore, to find the heights lying on the legs, you need to use the modified Pythagorean formula: a = √ (c 2 - b 2), where a, b are the legs (a is the leg to be found), c is the length of the hypotenuse. In order to find the second height, you need to put the resulting value a in place b. To find the third, lying inside the triangle, the height, the following formula is applied: h = 2s / a, where h is the height of a right-angled triangle, s is its area, a is the length of the side to which the height will be perpendicular.
A triangle is called acute-angled if all of its corners are acute. In this case, all three heights are located inside an acute-angled triangle. A triangle is called obtuse when there is one obtuse angle. The two heights of an obtuse triangle are outside the triangle and fall on the continuation of the sides. The third side is inside the triangle. Height is determined using the same Pythagorean theorem.
General formulas like calculating the height of a triangle
- The formula for finding the height of a triangle through the sides: H = 2 / a √p * (pc) * (pb) * (pb), where h is the height to be found, a, b and c are the sides of this triangle, p is its semi-perimeter,.
- Formula for finding the height of a triangle through angle and side: H = b sin y = c sin ß
- The formula for finding the height of a triangle through the area and side: h = 2S / a, where a is the side of the triangle, and h is the height plotted to side a.
- Formula for finding the height of a triangle in terms of radius and sides: H = bc / 2R.
how to find the height in a triangle if all three sides are given and got the best answer
Answer from Vusat Jafarov [active]
In short, do this: find the area by the formula S = under the root p * (pa) * (pb) * (pc), p is a half-perimeter, we find it like this 15 + 13 + 14 = 42, this is a pyrimeter and a half-pyrimeter is half a pyrimeter = 21 , And a, b, c are sides, a = 15, b = 13, c = 14, and we get S = under the root 21 * (21-15) * (21-13) * (21-14), we get S = under the root 21 * 6 * 8 * 7, S = root of 7056, S = 84 !!! now we find the height from the formula S = 1/2 base times the height, base-CE; 84 = 1/2 * 14 * h, 84 = 7 * h, h = 84/7, h = 12. Answer: height = 12 !!!
Answer from User deleted[newbie]
That's why I sometimes feel low! I'm 19 years old, and I can't solve this problem for 3rd grade, fucked up! It's a shame!
Answer from Al0253[guru]
Cut out the suspension. Divide by the specific gravity of the paper. Divide by paper thickness. Divide by the length of the base of the triangle. The height will turn out ...
Answer from Engineer[guru]
First, according to Heron, we determine the area of the triangle through its sides.
Well, then you yourself will guess.
Answer 84
Answer from LILU[active]
The height divides the base into two equal parts, and then use the Pythagorean theorem. But in principle, you are a lazy person.
Answer from IomoN[guru]
Thank you - "I remembered my childhood GOLD"))
Answer: the height is 12 cm. And the solution ... VERY simple) ... No formulas at all) ... But by the Pythagorean theorem.
You draw a triangle ... together with the height ... Now you see 2 triangles "inside the original".
The CE base - on which point M is located.
If we designate the distance CM = X, then the distance MU = (14-X).
Now we find X, if we equate the calculation of the height of these two triangles (the square root on both the left and right sides of the equality - I immediately "remove"). We get:
15 * 15-X * X = 13 * 13- (14-X) * (14-X) ... If you decide correctly, then CM = X = 9 cm.
Then the required height is DM * DM = 15 * 15-9 * 9 = 225-81 = 144.
Take the square root ... and DM = 12 cm.
Answer from 2 answers[guru]
Hey! Here is a selection of topics with answers to your question: how to find the height in a triangle if all three sides are given
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To solve many geometric problems, you need to find the height of a given figure. These tasks are of practical importance. When carrying out construction work, determining the height helps to calculate the required amount of materials, as well as determine how accurately the slopes and openings are made. Often, to build patterns, you need to have an idea of \ u200b \ u200bthe properties.
Many people, despite good grades in school, when building ordinary geometric shapes, the question arises of how to find the height of a triangle or parallelogram. Moreover, it is the most difficult. This is because a triangle can be sharp, obtuse, isosceles, or right-angled. Each of them has its own rules of construction and calculation.
How to find the height of a triangle in which all corners are sharp, graphically
If all the angles of the triangle are sharp (each angle in the triangle is less than 90 degrees), then to find the height, you need to do the following.
- According to the specified parameters, we carry out the construction of a triangle.
- Let us introduce the notation. A, B and C will be the tops of the figure. The angles corresponding to each vertex are α, β, γ. The sides opposite these corners are a, b, c.
- The height is called the perpendicular, lowered from the apex of the angle to the opposite side of the triangle. To find the heights of the triangle, we construct perpendiculars: from the vertex of the angle α to side a, from the vertex of the angle β to side b, and so on.
- The point of intersection of the height and side a will be denoted by H1, and the height itself will be h1. The intersection point of the height and side b will be H2, the height is respectively h2. For side c, the height will be h3, and the intersection point will be H3.
Height in an obtuse triangle
Now let's look at how to find the height of a triangle if there is one (more than 90 degrees). In this case, the height drawn from an obtuse angle will be inside the triangle. The other two heights will be outside the triangle.
Let the angles α and β in our triangle be acute, and the angle γ obtuse. Then, to plot the heights outgoing from the angles α and β, it is necessary to extend the opposite sides of the triangle in order to draw the perpendiculars.
How to find the height of an isosceles triangle
Such a figure has two equal sides and a base, while the angles at the base are also equal to each other. This equality of sides and angles makes it easier to plot and calculate heights.
First, let's draw the triangle itself. Let the sides b and c, as well as the angles β, γ, be respectively equal.
Now we draw the height from the vertex of the angle α, we denote it by h1. For this height will be both the bisector and the median.
Only one construction can be made for the foundation. For example, draw the median - a segment connecting the top of an isosceles triangle and the opposite side, the base, to find the height and bisector. And to calculate the length of the height for the other two sides, you can only build one height. Thus, to graphically determine how to calculate the height of an isosceles triangle, it is enough to find two out of three heights.
How to find the height of a right triangle
It is much easier to determine the heights of a right-angled triangle than others. This is because the legs themselves make up a right angle, which means they are heights.
To build the third height, as usual, a perpendicular is drawn connecting the vertex of the right angle and the opposite side. As a result, in order for a triangle in this case, only one construction is required.
