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The most popular triangle used in construction, engineering and mathematics is the right triangle, which has a 90o angle at the base. We'll call your base "x", height "y" and diagonal (hypotenuse) "r".
You can find these values using your calculator's trigonometric functions, or you can use the Pythagorean Theorem.
Finding Values (Pythagorean Theorem):
The Pythagorean Theorem is straightforward and states that, for a right triangle, r^2 = x^2 + y^2. We can use a little bit of algebra to find x, y and r.
r = sqrt(x^2 + y^2)
r^2 = x^2 + y^2
r = sqrt(x^2 + y^2); remove the ^2 from r
x = sqrt(r^2 - y^2)
r^2 = x^2 + y^2
r^2 - y^2 = x^2; move y^2 to the left side of the equation
sqrt(r^2 - y^2) = x; remove the ^2 from x
y = sqrt(r^2 - x^2)
r^2 = x^2 + y^2
r^2 - x^2 = y^2; move x^2 to the left side of the equation
sqrt(r^2 - x^2) = y; remove the ^2 from y
Finding Values (Trigonometric Functions):
Acquiring Ratios:
cos(angle) = x/r
sin(angle) = y/r
tan(angle) = y/x
Acquiring Angles:
cos-1(x/r) = angle
sin-1(y/r) = angle
tan-1(y/x) = angle
That looks confusing. What are cos, sin, tan, etc?
They're functions. You give a function input and it outputs something else. How they do this is complicated and required calculus.
x = cos(angle) * r
cos(angle) = x/r
cos(angle) * r = x; move r to the left side of the equation
y = sin(angle) * r
sin(angle) = y/r
sin(angle) * r = y; move r to the left side of the equation
x = 1 / (tan(angle)/y)
tan(angle) = y/x
tan(angle) / y = 1/x; move y to the left side of the equation
1 / (tan(angle) / y) = x; flip the equation
y = tan(angle) * x
tan(angle) = y/x
tan(angle) * x = y; move x to the left side of the equation
r = 1 / (cos(angle)/x)
cos(angle) = x/r
cos(angle) / x = 1/r; move x to the left side of the equation
1 / (cos(angle)/x) = r; flip the equation
r = 1 / (sin(angle)/y)
sin(angle) = y/r
sin(angle) / y = 1/r; move y to the left side of the equation
1 / (sin(angle)/y) = r; flip the equation
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How do you find the perimeter of a scalene triangle?
-- Find the length of one side. -- Find the length of another side. -- Find the length of the remaining side. -- Add the three numbers. -- Their sum is the perimeter of the scalene triangle.
How do you find the length of a triangle when perimeter is given?
If the triangle is equilateral, you simply divide the perimeter by three to find the length of each side. If the triangle is not equilateral, you will need more information to determine the length of each side.
How do you find the height of an equalateral triangle?
To find the altitude or height of an equilateral triangle, take one-half of the length of a side of the triangle and multiple by "square root" of 3. So, if for example, the side has length 10, the height = 5 Square root of 3.
How do you find the side length on a triangle with one angle given?
To find side lengths on a triangle, you need to know at least one of the sides. The possible combinations for solving* a triangle are: side, side, side; side, angle, side; angle, side, angle; angle, side, longer side. *To solve a triangle is to find the lengths of all the sides and the measures of all the angles.
11 abc is an equilateral triangle with side length equal to 50 cm bh is perpendicular to ac mn is parallel to ac find the area of triangle bmn if the length of mn is equal to 12 cm?
ABC is an equilateral triangle with side length equal to 50 cm. BH is perpendicular to AC. MN is parallel to AC. Find the area of triangle BMN if the length of MN is equal to 12 cm.
How do you find the midsegment of a triangle?
A midsegment of a triangle is parallel to the side of the triangle, and it's length is half the length of that side
A radius of a regular triangle is 12 Find the length of one side of the triangle?
A radius of a regular triangle is 12 . find the length of one side of the triangle?
HOW do you find the similar ratio of a triangle?
Divide the length of a side of one triangle by the length of the corresponding side of the other triangle.
How do you find the perimeter of a scalene triangle?
-- Find the length of one side. -- Find the length of another side. -- Find the length of the remaining side. -- Add the three numbers. -- Their sum is the perimeter of the scalene triangle.
How do you find the length of a triangle when perimeter is given?
If the triangle is equilateral, you simply divide the perimeter by three to find the length of each side. If the triangle is not equilateral, you will need more information to determine the length of each side.
Show how to find scale factor of a small triangle to a larger similar triangle?
The ratio of the length of the side in the big triangle to the length of the corresponding side in the little triangle is the scale factor.
How do you find Ares and perimeter on a tringle?
-- Area of a triangle = 1/2 of (length of the base times height) -- Perimeter of a triangle = (length of one side) + (length of another side) + (length of last side)
How do i find the Ratio of the shortest to the longest side of a triangle?
You divide the length of the shortest side by the length of the longest side.
How do you find the side length of a right triangle if you have one side length?
One side is not enough. For a right triangle the third side can be calculated by Pythagoras' Theorem if you know the length of any two sides.
How do you find the length of one side of a triangle?
The answer depends on what information you do have.
What is pythagorean thorem for?
The Pythagorean theorem is used to find the length of a certain side in a right triangle. If you know the length of two sides of a right triangle, you can use the Pythagorean theorem, a2+ b2 = c2, to find the length of the other side. In the formula, c is the hypotenuse, which the longest side of the triangle.
How do you find the side of an isosceles triangle?
An isosceles triangle has 3 sides 2 of which are equal in length
