 # Question: How Do You Find The Height Of A Triangle Given Two Sides?

## How do you find the third side of a triangle given two sides?

Just like the Law of Sines, the Law of Cosines works for any triangle, not just right triangles.

In particular, the Law of Cosines can be used to find the length of the third side of a triangle when you know the length of two sides and the angle in between.

To use the Law of Sines to find a third side: 1..

## How do you find the length of a triangle given two sides?

Right Triangles and the Pythagorean TheoremThe Pythagorean Theorem, a2+b2=c2, a 2 + b 2 = c 2 , can be used to find the length of any side of a right triangle.The side opposite the right angle is called the hypotenuse (side c in the figure).More items…

## How do you find the height of an isosceles triangle?

We can find the height by splitting the isosceles triangle into two right-angled triangles and then applying Pythagoras’ Theorem to one of them. We now know the height of the triangle and can use this to go back and find the area of the isosceles triangle.

## What is the rule for side lengths of a triangle?

According to the first triangle inequality theorem, the lengths of any two sides of a triangle must add up to more than the length of the third side. This means that you cannot draw a triangle that has side lengths 2, 7 and 12, for instance, since 2 + 7 is less than 12.

## Does 1/2 base times height work for all triangles?

For instance, there’s the basic formula that the area of a triangle is half the base times the height. This formula only works, of course, when you know what the height of the triangle is. … That is to say, the area of a triangle is half the product of two sides times the sine of the included angle.

## How do I find the missing length of a triangle?

Finding the missing side of a right triangle is a pretty simple matter if two sides are known. One of the more famous mathematical formulas is a2+b2=c2 a 2 + b 2 = c 2 , which is known as the Pythagorean Theorem.

## What are the formulas for triangles?

The area of a triangle is equal to: (the length of the altitude) × (the length of the base) / 2. In ∆ABC, BD is the altitude to base AC and AE is the altitude to base BC. Triangle Formula: The area of a triangle ∆ABC is equal to ½ × BD × AC = ½ × 5 × 8 = 20. The triangle area is also equal to (AE × BC) / 2.

## How do you find the height in a triangle?

A right triangle is a triangle with one angle equal to 90°. Two heights are easy to find, as the legs are perpendicular: if the shorter leg is a base, then the longer leg is the altitude (and the other way round). The third altitude of a triangle may be calculated from the formula: hᶜ = area * 2 / c = a * b / c.

## How do you find the base and height 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 the height of a right triangle?

The height of a triangle is the distance from the base to the highest point, and in a right triangle that will be found by the side adjoining the base at a right angle.