How To Find The Height Of A Triangle

What is the formula of height?

Full height = present heightpercentage of full height at current age x 100.Q. Identify the formulas which is used to calculate net force?

What is the formula for calculating triangle?

Area of a Triangle Formula – The area of the triangle is given by the formula mentioned below:

Area of a Triangle = A = ½ (b × h) square units

where b and h are the base and height of the triangle, respectively. Now, let’s see how to calculate the area of a triangle using the given formula. The area formulas for all the different types of triangles, like an area of an equilateral triangle, right-angled triangle, an isosceles triangle along with how to find the area of a triangle with 3 sides using Heron’s formula with examples are given below.

How do you find the height of a triangle if not given?

Download Article Download Article To calculate the area of a triangle you need to know its height. To find the height follow these instructions. You must at least have a base to find the height.

1. 1 Recall the formula for the area of a triangle. The formula for the area of a triangle is A=1/2bh,
   • A = Area of the triangle
   • b = Length of the base of the triangle
   • h = Height of the base of the triangle
2. 2 Look at your triangle and determine which variables you know. You already know the area, so assign that value to A, You should also know the value of one side length; assign that value to “‘b'”. Any side of a triangle can be the base, regardless of how the triangle is drawn. To visualize this, just imagine rotating the triangle until the known side length is at the bottom. Example If you know that the area of a triangle is 20, and one side is 4, then: A = 20 and b = 4, Advertisement
3. 3 Plug your values into the equation A=1/2bh and do the math. First multiply the base (b) by 1/2, then divide the area (A) by the product. The resulting value will be the height of your triangle! Example 20 = 1/2(4)h Plug the numbers into the equation.20 = 2h Multiply 4 by 1/2.10 = h Divide by 2 to find the value for height.

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1. 1 Recall the properties of an equilateral triangle. An equilateral triangle has three equal sides, and three equal angles that are each 60 degrees. If you cut an equilateral triangle in half, you will end up with two congruent right triangles.
   • In this example, we will be using an equilateral triangle with side lengths of 8.
2. 2 Recall the Pythagorean Theorem, The Pythagorean Theorem states that for any right triangle with sides of length a and b, and hypotenuse of length c : a 2 + b 2 = c 2, We can use this theorem to find the height of our equilateral triangle!
3. 3 Break the equilateral triangle in half, and assign values to variables a, b, and c, The hypotenuse c will be equal to the original side length. Side a will be equal to 1/2 the side length, and side b is the height of the triangle that we need to solve.
   • Using our example equilateral triangle with sides of 8, c = 8 and a = 4,
4. 4 Plug the values into the Pythagorean Theorem and solve for b 2, First square c and a by multiplying each number by itself. Then subtract a 2 from c 2, Example 4 2 + b 2 = 8 2 Plug in the values for a and c.16 + b 2 = 64 Square a and c. b 2 = 48 Subtract a 2 from c 2,
5. 5 Find the square root of b 2 to get the height of your triangle! Use the square root function on your calculator to find Sqrt( 2, The answer is the height of your equilateral triangle!
   • b = Sqrt (48) = 6.93

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1. 1 Determine what variables you know. The height of a triangle can be found if you have 2 sides and the angle in between them, or all three sides. We’ll call the sides of the triangle a, b, and c, and the angles, A, B, and C.
   • If you have all three sides, you’ll use Heron’s formula, and the formula for the area of a triangle.
   • If you have two sides and an angle, you’ll use the formula for the area given two angles and a side. A = 1/2ab(sin C).
2. 2 Use Heron’s formula if you have all three sides. Heron’s formula has two parts. First, you must find the variable s, which is equal to half of the perimeter of the triangle. This is done with this formula: s = (a+b+c)/2. Heron’s Formula Example For a triangle with sides a = 4, b = 3, and c = 5: s = (4+3+5)/2 s = (12)/2 s = 6 Then use the second part of Heron’s formula, Area = sqr(s(s-a)(s-b)(s-c). Replace Area in the equation with its equivalent in the area formula: 1/2bh (or 1/2ah or 1/2ch). Solve for h. For our example triangle this looks like: 1/2(3)h = sqr(6(6-4)(6-3)(6-5).3/2h = sqr(6(2)(3)(1) 3/2h = sqr(36) Use a calculator to calculate the square root, which in this case makes it 3/2h = 6. Therefore, height is equal to 4, using side b as the base.
3. 3 Use the area given two sides and an angle formula if you have a side and an angle. Replace area in the formula with its equivalent in the area of a triangle formula: 1/2bh. This gives you a formula that looks like 1/2bh = 1/2ab(sin C). This can be simplified to h = a(sin C), thereby eliminating one of the side variables. Note that angle C and side a are both positioned across from the height that you need to find (both on the right side from it, or both on the left side). Finding Height with 1 Side and 1 Angle Example For example, with a = 3, and C = 40 degrees, the equation looks like this: h = 3(sin 40) Use your calculator to finish the equation, which makes h roughly 1.928.

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What is the height and base of a triangle?

The area of a triangle is ½ (b × h), where b is the base and h is the height. The base of a triangle is any one of the sides, and the height of the triangle is the length of the altitude from the opposite vertex to that base.

What is a triangle with 3 different sides?

Angle Sum Property of a Triangle – The sum of all three internal angles of a scalene triangle is 180°. It is also known as the angle sum property of the triangle. In $\Delta\text, ∠\text + ∠\text + ∠\text = 180°$ The difference in the sides or the angles do not affect the basic properties of a triangle. For example: In $\Delta\text, ∠\text = 60°, ∠\text = 70°$ By the angle sum property of a triangle $∠\text + ∠\text + ∠\text = 180°$ $60° + 70° + ∠\text = 180°$ $130° + ∠\text = 180°$ $∠\text = 50°$

What is the formula for the height of an equilateral triangle?

The altitude of Equilateral Triangle Formula: h = (1/2) * √3 * a. Angles of Equilateral Triangle: A = B = C = 60 degrees.

How to find the height of an isosceles triangle without area?

Answer and Explanation: To find the height of an isosceles triangle, we square the length of one of the equal sides and subtract the square of half the base. We then find the square root of the result of the subtraction.

What is the height of each triangle?

Summary – A height of a triangle is a perpendicular segment between the side chosen as the base and the opposite vertex. We can use tools with right angles to help us draw height segments. An index card (or any stiff paper with a right angle) is a handy tool for drawing a line that is perpendicular to another line.

Choose a side of a triangle as the base. Identify its opposite vertex. Line up one edge of the index card with that base. Slide the card along the base until a perpendicular edge of the card meets the opposite vertex. Use the card edge to draw a line from the vertex to the base. That segment represents the height.

Figure \(\PageIndex \) Sometimes we may need to extend the line of the base to identify the height, such as when finding the height of an obtuse triangle, or whenever the opposite vertex is not directly over the base. In these cases, the height segment is typically drawn outside of the triangle. Figure \(\PageIndex \) Even though any side of a triangle can be a base, some base-height pairs can be more easily determined than others, so it helps to choose strategically. For example, when dealing with a right triangle, it often makes sense to use the two sides that make the right angle as the base and the height because one side is already perpendicular to the other. Figure \(\PageIndex \)

What is the formula for base and height?

Answer: If area and base are given: height = 2A/ b = (2 × Area) / base. If area and height are given: base = 2A/ h = (2 × Area) / height – Let’s find the base and height of a triangle when only the area is known. Explanation: Area of a triangle = 1/2 × Base × Height If area and base of the triangle are given: height = 2A/ b = (2 × Area) / base If area and height of the triangle are given: base = 2A/ h = (2 × Area) / height But for the equilateral triangle, height and base are interconnected:

Area = √3/4 a 2 height = √3/2 a

So, from the area of the equilateral triangle calculate the side, then find the height of the triangle using the formula.

Is the height of a triangle equal to the base?

Height of an equilateral triangle is not equal to the base of an equilateral triangle. It is a multiple of the side of an equilateral triangle, given as h = 3 2 a.

How to find the maximum length of the third side of a triangle?

Minimum and maximum possible length of the third side of a triangle
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Given two sides of a triangle s1 and s2, the task is to find the minimum and maximum possible length of the third side of the given triangle. Print -1 if it is not possible to make a triangle with the given side lengths. Note that the length of all the sides must be integers.

1. s1 + s2 > s3
2. s1 + s3 > s2
3. s2 + s3 > s1

Solving for s3, we get s3 < s1 + s2, s3 > s2 – s1 and s3 > s1 – s2, It is clear now that the length of the third side must lie in the range (max(s1, s2) – min(s1, s2), s1 + s2) So, the minimum possible value will be max(s1, s2) – min(s1, s2) + 1 and the maximum possible value will be s1 + s2 – 1,Below is the implementation of the above approach:

#include using namespace std; void find_length( int s1, int s2) int max_length = s1 + s2 – 1; int min_length = max(s1, s2) – min(s1, s2) + 1; if (min_length > max_length) cout << "Max = " << max_length << endl; cout << "Min = " << min_length; } int main()

table>

import java.io.*;
• class GFG
• int max_length = s1 + s2 – 1 ;

int min_length = Math.max(s1, s2) – Math.min(s1, s2) + 1 ; if (min_length > max_length) System.out.println( “Max = ” + max_length); System.out.print( “Min = ” + min_length);

• }
• public static void main (String args)
• }

table>

1. def find_length(s1, s2) :
2. if (s1 < = 0 or s2 < = 0 ) :
3. print ( – 1, end = “”);
4. return ;
5. max_length = s1 + s2 – 1 ;
6. min_length = max (s1, s2) – min (s1, s2) + 1 ;
7. if (min_length > max_length) :
8. print ( – 1, end = “”);
9. return ;
10. print ( “Max =”, max_length);
11. print ( “Min =”, min_length);
12. if _name_ = = “_main_” :
13. s1 = 8 ;
14. s2 = 5 ;
15. find_length(s1, s2);

table>

• using System;
• class GFG
• int max_length = s1 + s2 – 1;

int min_length = Math.Max(s1, s2) – Math.Min(s1, s2) + 1;

1. if (min_length > max_length)
2. Console.WriteLine( “Max = ” + max_length);
3. Console.WriteLine( “Min = ” + min_length);
4. }
5. public static void Main ()
6. }

table>

Time Complexity: O(1) Auxiliary Space: O(1)

• Last Updated : 07 Jun, 2022
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How to find the length of a side of a triangle with 3 angles?

Apply the law of sines or trigonometry to find the right triangle side lengths: a = c × sin(α) or a = c × cos(β)