In a right triangle abc, cd is an altitude, such that ad=bc. find ac, if ab=3 cm, and cd=2 cm.

We are going to use the concept that area of any given triangle can be written as 1/2 * Base * Height .

Area of shown Triangle can be written as =

We know  AB = 3 and CD =2

Lets say  BC = X  so BD =3 - X

In right triangle  BCD,

Using Pythagorean :

                                  X=

                                 BC=

Now use the Area equation :

                          AC  * BC   = AB * CD

The length of AC =

Triangles are flat fields bounded by 3 intersecting sides and 3 angles

This side can be the same length or different.

If at an angle there is an angle of 90 degrees, this triangle is said to be a right angle

There is a hypotenuse in this triangle which is the sum of the two sides

where c = hypotenuse

This formula is known as the Pythagorean theorem which states that:

" the hypotenuse or the longest side in a right triangle equal to the sum of the squares of the other sides".

A right triangle ABC, CD is an altitude, such that AD = BC. AB = 3 cm, and CD = 2 cm.

The CD line divides the ABC triangle into two ADC and BDC triangles

BD = 3-x

CB = x

CD = 2

We use the Pythagorean theorem

CB² = BD² + CD²

x² = (3-x)² + 2²

x² = 9-6x + x² + 4

6x = 13

x = 13/6

So length CB = 13/6

because AD = CB, the length AD = 13/6

CD = 2

We use the Pythagorean theorem

CD² + AD² = AC²

2² + (13/6)² = AC²

4 + 169/36 = AC²

313/36 = AC²

trigonometric ratio

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Prove the converse of the Pythagorean Theorem

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Use Pythagoras' theorem

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Keywords: Pythagoras' theorem, hypotenuse,altitude, right triangle

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step-by-step explanation: