How to Find the Height of a Scalene Triangle

Scalene Triangle:
A triangle in which each side of different length and different angles.

Scalene Triangle

In the given figure AB#BC#CA,therefore the triangle ABC is an scalene triangle. Th three sides measures of different length.

Properties of Scalene Triangle
No sides are symmetry
The angles are not equal 

Types of Scalene Triangle:
Right angled scalene triangle: The triangle in which one of the angle is right angle.
Obtuse angled scalene triangle: The triangle in which one of the angle is obtuse angle.
Acute Scalene Triangle: The three angles of triangle are acute and three sides are of different lengths.

Perimeter of  Triangle:
Sum of the sides of the triangle gives Perimeter of Scalene triangle.
AB + BC + CA = Perimeter

Perimeter of Triangle

Area of Scalene Triangle:
Area = $\frac{1}{2}$ base* height
Length of any side of the given triangle is taken as base and the corresponding altitude is named as height.
When length of the three sides are given are of triangle is given by  Heron's formula
Area = $\sqrt{s(s-a)(s-b)(s-c)}$
where a,b and c  are the lengths of the sides of the triangle

Height of Scalene Triangle:
The height of scalene triangle can be determined using Pythagoras theorem. The height of a triangle is the perpendicular distance to the base from the vertex to opposite the base.
Example: To find the height of scalene triangle whose base is 21m, longest side is 20m and shortest side is 13m.

Solution: Given the base of triangle is 21m, longest side is 20m and shortest side is 13m.

Height of Scalene Triangle

The triangle is divided into two, use Pythagoras theorem to find height of the triangle.
From the figure triangle ABD is given as:
AB2 = BD+ AD2
(20)2 = (21-x)+ h2
(400) = (21)+ (x)2 - 2*21*x + h2
400 = 441 + x2 - 42x + h2    --------(1)

Smaller triangle ADC is given as:
AC2 = AD+ DC2
(13)2 = h2 + x2
(13)2  - x= h2 ---------(2)
assign the value of h in equation (1)
400 = 441 + x2 - 42x + (13)2  - x2                       // simplify   //
400 = 441 - 42x + 169
400 = 610 - 42x
400 - 610 = -42 x
 -210 = -42x
   5 = x

Assign the value of x in equation 2
(13)2  - 52 = h2
169 - 25 =  h2
144  =  h2
12 = h
height of scalene triangle is 12 m

Best Results From Yahoo Answers Youtube

From Yahoo Answers

Question:How would i go about to finding the height of a scalene triangle with only one side and all three angles? I have a triangle w/ A, 45, B, 75, C,60 degress. the length between AB is 570.

Answers:1: draw a diagram. To make it easy to follow, lets call the left angle A, the top angle B and the right angle C 2: Draw a vertical line from B to the baseline (AC) bisecting the triangle. 3: You can now use the sine rule to find the height- sin A = opposite (the height h of the original triangle) over hypotenuse sin 45 = h/570 h = 570. sin45 h = 485

Question:Please break it down into simple terms. Lets say it's 6x4x1 triangle The height is not the side, but how do you get the height based on three 3 figures you do know? LETS JUST ASSUME I don't know what all these a, b, cos, and more MEAN... Now, still looking for a good answer...

Answers:First, 6-4-1 is not a triangle. The sum of each pair of sides must be greater than the third. 4+1 < 6 so this is not a triangle. Lets take 2-3-4. [Note that this is not a right triangle.] First, decide which height you want. Let's take the one perpendicular to the side of length 4. Find one of the two angles adjacent to that side using the law of cosines. We'll find the one between 3 and 4: c = a + b - 2ab cos C 2 = 3 + 4 - 2(3)(4) cos C cos C = 0.875 C 28.96 degrees Now, the height is the adjacent side (3) times sin C: h = 3 sin 28.96 1.452 EDIT: I'm using standard, well known and widely-used notation for triangles. Lowercase a, b, c represent the length of threes sides of a triangle. Uppercase A represents the angle opposite side a; likewise for B and C. Sin and cos are the sine and cosine of the angle, which can be found on any scientific calculator. I'm sorry, but there is no simpler answer for acute triangles. EDIT 2: I realized that my example is an obtuse triangle, but the formula works the same for any triangle: obtuse, right, or acute. 4-5-6 is acute.

Question:How do I find the perimeter of a scalene triangle using only one measurement? The only measurement I know is 5, and the triangle has an area of 24. What formula, etc, should I use to find the perimeter?

Answers:u have one side and the area, from that you can find the height, the length of the segment that is perpendicular to the side you know the length of, and goes through the opposite vertex. a=(1/2)bh. Then you have two right triangles, simply use the pythagorean therom and you get the other sides.

Question:the base is 11 in., and the height is 7 in. i know you have to use the Pythagorean theory, but i need to see the steps.

Answers:I assume base is NOT the hypotenuse, AB=base=11 BC=7,one side is base AC=hypotenuse=\/''''''49 +121''''=\/''''170''''=13.038 God bless you.

From Youtube

Constructing a Scalene Triangle :The video describes how to construct an scalene triangle.