[sqrtrac34] is the area of an equilateral triangle.

### Triangle Formula Example

Method 1: We look at the third row of the Pascals Triangle because n is three and the second column of the Pascals Triangle because the power of y is two in the phrase xy2. So the number in Pascal's Triangle is three. However, since the power of x is 2 and y is 1 in the phrase xy2, the Pascal Triangles number will be multiplied by 21 and 12 to obtain the coefficient. 3 x 21 x 12 = 6 Coefficient Method 2: We just use nC r for n = 3 and r = 2. In the expansion of (2x + y)3, the Pascal Triangle number of term xy2 is 3C 2 = 3. However, since the power of x is 2 and y is 1 in the phrase xy2, the Pascal Triangles number will be multiplied by 21 and 12 to obtain the coefficient. 3 x 21 x 12 = 6 Coefficient

A triangle's height is the segment traced from a vertex perpendicular to the side opposite that vertex. The opposing side is referred to as the base in relation to that vertex and height. A triangle's area is equal to (the length of the height) / (the length of the base) / 2.

Solution The perimeter is the sum of the lengths of the triangle's three sides. Because all three sides of an equilateral triangle have the same length, we may divide the perimeter by three to obtain the length of one of its sides. As a result, we know that the length of one of the triangle's sides is 30/3=10. We can now plug that length into the height formula and get: $$ h = racsqrt3a2 $$ $$ h= racsqrt3(10)2 $$ $$ $latex h = 8.66$ The triangle's height is 8.66 in. 6th EXAMPLE Determine the height of an equilateral triangle with a perimeter of 21 in.

As you can see, calculating the area of the triangle given the values of base and height is much simpler. The above-mentioned strategies and formulas are applicable to the computation of all forms of triangle areas. So, please feel free to use this formula for personal or academic use. Scholars may provide this method to others to assist them in determining the area of a triangle.

### 45 45 90 Triangle Formula Examples

Knowing you'll need to remember these numbers, you may either memorize them or redraw this triangle and utilize SOHCAHTOA to assist you get the angle's ratios. In any case, we hope that by describing the triangle's components to you, you now have a better knowledge of the 45 45 90 unusual triangle and how its ratios came about.

Triangle 45-45-90 A 45-45-90 triangle is a particular right triangle. 30-60-90 is another sort of special right triangle. These values indicate the angles' degree measurements. Because the ratios of their sides are always the same, these triangles are considered exceptional. Special right triangles have a wide range of applications in geometry and trigonometry. This course will teach you the basic formula for ratios as well as how to locate the missing sides of any 30 60 90 right triangle. We also provide a free study guide that outlines the processes in detail on one page! The triangle's fundamental ratios are shown in the example below. The ratios will always be true regardless of the " x " value. Because both base angles are equal to 45, the reverse of the isosceles triangle theorem states that both legs are equal. As a result, the two congruent sides will be referred to as legs, and the other side (opposite the right angle) as the hypotenuse. The pythagorean theorem provides further information about the hypotenuse.

### 30 60 90 Triangle Formula Examples

To properly solve our right triangle as a 30 60 90, we must first identify the triangle's three angles to be 30, 60, and 90. A minimum of one side length must already be known in order to solve for the side lengths. If we know we're dealing with a right triangle, one of the angles must be 90 degrees. It is proved to be a 30 60 90 triangle if another angle is either 30 or 60 degrees. This is due to the fact that the interior angles of a triangle always amount to 180 degrees.

The side opposing the 30 degree angle will always be the shortest in length. The opposing side of the 60-degree angle will be three times as long. The opposing side of the 90-degree angle will be twice as long. Remember that the shortest side will be opposite the smallest angle, and the longest will be opposite the greatest. How do you solve the unique right triangle?

Using the equilateral triangle's attributes Did you note how our triangle of interest is only half of an equilateral triangle? If you recall the formula for the height of such a regular triangle, you can calculate the length of the second leg. It is equivalent to side divided by a square root of 3: h = c3/2, h = b, and c = 2a, therefore b = c3/2 = a32. Making use of trigonometry

Knowing the fundamental concepts of sine, cosine, and tangent makes it relatively straightforward to determine the value for these in any 30-60-90 triangle. Sine, cosine, and tangent all indicate a ratio of a triangle's sides depending on one of the angles, theta or (