You need to calculate the length of one side of a triangle when either the lengths of two sides are known or one angle and the length of a side are known.

Use the `Math.Sin`

,
`Math.Cos`

, and `Math.Tan`

methods
of the `Math`

class to find the length of one side.
The equations for these methods are as follows:

double theta = 40; double hypotenuse = 5; double oppositeSide; double adjacentSide; oppositeSide = Math.Sin(theta) * hypotenuse; oppositeSide = Math.Tan(theta) * adjacentSide; adjacentSide = Math.Cos(theta) * hypotenuse; adjacentSide = oppositeSide / Math.Tan(theta); hypotenuse = oppositeSide / Math.Sin(theta); hypotenuse = adjacentSide / Math.Cos(theta);

where `theta`

(Θ) is the known angle, and the `oppositeSide`

variable
is equal to the length of the side *opposite* to
the angle `theta`

, and the
`adjacentSide`

variable is equal to the length of
the side *adjacent* to the angle
`theta`

. The `hypotenuse`

variable
is equal to the length of the *hypotenuse* of the
triangle. See Figure 1-1.

In addition to these three static methods, the length of the
hypotenuse of a right triangle can be calculated using the
Pythagorean theorem. This theorem states
that the hypotenuse of a right triangle is equal to the square root
of the sum of the squares of the other two sides.
This
equation can be realized through the use of the
`Math.Pow`

and `Math.Sqrt`

static
methods of the `Math`

class, as follows:

double hypotenuse = Math.Sqrt(Math.Pow(xSide, 2) + Math.Pow(ySide, 2))

where `xSide`

and `ySide`

are the
lengths of the two sides that are *not* the
hypotenuse of the triangle.

Finding the length of a side of a right triangle is easy when an angle and the length of one of the sides are known. Using the trigonometric functions sine, cosine, and tangent, we can derive the lengths of either of the two unknown sides. The equations for sine, cosine, and tangent are defined here:

sin(Theta) = oppositeSide / hypotenuseSide cos(Theta) = adjacentSide / hypotenuseSide tan(Theta) = oppositeSide / adjacentSide

where `theta`

is the value of the known angle.
Rearranging these equations allows us to derive the following
equations:

oppositeSide = sin(theta) * hypotenuse; oppositeSide = tan(theta) * adjacentSide; adjacentSide = cos(theta) * hypotenuse; adjacentSide = oppositeSide / tan(theta); hypotenuse = oppositeSide / sin(theta); hypotenuse = adjacentSide / cos(theta);

These equations give us two methods to find the length of each side of the triangle.

In the case where none of the angles are known, but the lengths of two of the sides are known, use the Pythagorean theorem to determine the length of the hypotenuse. This theorem is defined as follows:

Math.Sqrt(Math.Pow(hypotenuse)) = Math.Sqrt(Math.Pow(xSide, 2) + Math.Pow(ySide, 2))

Simplifying this equation into a syntax usable by C#, we obtain the following code:

double hypotenuse = Math.Sqrt(Math.Pow(xSide, 2) + Math.Pow(ySide, 2));

where `hypotenuse`

is equal to the length of the
hypotenuse, and `xSide`

and `ySide`

are the lengths of the other two sides.

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