How to Find Sine Angle When You Know O and H

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To summate the area of a triangle y'all need to know its height. To detect the meridian follow these instructions. Y'all must at to the lowest degree have a base to detect the height.

1. one

   Recall the formula for the surface area of a triangle. The formula for the area of a triangle is

   A=1/2bh.

   ^[1]

   • A = Expanse of the triangle
   • b = Length of the base of the triangle
   • h = Height of the base of the triangle

2. 2

   Await at your triangle and determine which variables y'all know. You already know the area, so assign that value to A. You should also know the value of ane side length; assign that value to "'b'".

   Whatever side of a triangle tin be the base,

   regardless of how the triangle is fatigued. To visualize this, only imagine rotating the triangle until the known side length is at the bottom.

   Case
   If y'all know that the area of a triangle is twenty, and one side is iv, then:
   A = 20 and b = iv.

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3. 3

   Plug your values into the equation A=1/2bh and do the math. Start multiply the base (b) by 1/ii, and then split the surface area (A) past the production. The resulting value volition exist the pinnacle of your triangle!

   Example
   xx = 1/2(4)h Plug the numbers into the equation.
   xx = 2h Multiply 4 by i/2.
   x = h Divide by 2 to find the value for meridian.

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1. 1

   Recall the properties of an equilateral triangle. An equilateral triangle has 3 equal sides, and iii equal angles that are each 60 degrees. If you

   cutting an equilateral triangle in half, you will stop up with two coinciding right triangles.

   ^[2]

   • In this example, we volition be using an equilateral triangle with side lengths of eight.

2. 2

   Recall the Pythagorean Theorem. The Pythagorean Theorem states that for whatsoever right triangle with sides of length a and b, and hypotenuse of length c:

   a^two + b² = c² .

   We can utilise this theorem to notice the meridian of our equilateral triangle!^[3]

3. 3

   Break the equilateral triangle in half, and assign values to variables a, b, and c. The hypotenuse c volition exist equal to the original side length. Side a volition be equal to 1/2 the side length, and side b is the tiptop of the triangle that nosotros need to solve.

   • Using our instance equilateral triangle with sides of eight, c = eight and a = 4.

4. 4

   Plug the values into the Pythagorean Theorem and solve for bⁱⁱ. First square c and a by multiplying each number past itself. Then decrease a² from c².

   Example
   4^two + b² = 8² Plug in the values for a and c.
   16 + b² = 64 Square a and c.
   b^two = 48 Decrease a² from c^two.

5. 5

   Find the square root of bⁱⁱ to become the height of your triangle! Use the square root function on your calculator to discover Sqrt(². The answer is the height of your equilateral triangle!

   • b = Sqrt (48) = 6.93

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1. 1

   Decide what variables y'all know. The height of a triangle tin exist constitute if you take 2 sides and the angle in between them, or all iii sides. We'll call the sides of the triangle a, b, and c, and the angles, A, B, and C.

   • If you lot have all three sides, yous'll utilize

     Heron's formula

     , and the formula for the area of a triangle.
   • If you have two sides and an angle, yous'll utilize the formula for the surface area given two angles and a side.

     A = 1/2ab(sin C).^[four]

2. two

   Employ Heron'south formula if you take all three sides. Heron'south formula has two parts. First, you must detect the variable

   s, which is equal to half of the perimeter of the triangle.

   This is washed with this formula:

   due south = (a+b+c)/2.^[five]

   Heron's Formula Example
   For a triangle with sides a = four, b = 3, and c = v:
   s = (iv+3+five)/2
   s = (12)/2
   s = 6
   Then utilize the second function of Heron's formula, Area = sqr(s(southward-a)(due south-b)(south-c). Supercede Area in the equation with its equivalent in the area formula: 1/2bh (or 1/2ah or 1/2ch).
   Solve for h. For our instance triangle this looks like:
   ane/ii(3)h = sqr(6(6-4)(6-3)(half-dozen-five).
   3/2h = sqr(6(2)(iii)(1)
   3/2h = sqr(36)
   Use a calculator to calculate the foursquare root, which in this case makes it 3/2h = vi.
   Therefore, top is equal to iv, using side b as the base.

3. 3

   Use the area given two sides and an bending formula if you take a side and an bending. Replace area in the formula with its equivalent in the surface area of a triangle formula: 1/2bh. This gives you a formula that looks like 1/2bh = i/2ab(sin C). This can be simplified to

   h = a(sin C)

   , thereby eliminating 1 of the side variables.^[6]

   Finding Height with one Side and 1 Angle Example
   For example, with a = iii, and C = 40 degrees, the equation looks like this:
   h = 3(sin 40)
   Use your figurer to cease the equation, which makes h roughly 1.928.

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Add New Question

• Question

  How practice I observe the area of an equilateral triangle when only the height is given?

  

  H = height, South = side, A = expanse, B = base. You know that each angle is lx degrees considering information technology is an equilateral triangle. If you wait at 1 of the triangle halves, H/S = sin lx degrees because South is the longest side (the hypotenuse) and H is across from the 60 degree angle, so at present you tin discover S. The base of the triangle is S because all the sides are the aforementioned, so B = Due south. Using A = (1/2)*BH, you get A = (i/ii)*SH, which you can at present find.

• Question

  How do I calculate the peak of a right triangle, given simply the length of the base and the interior angle at the base?

  

  Look up the tangent of the bending in a trigonometry table. Multiply the tangent past the length of the base.

• Question

  How do I make up one's mind the height of a triangle when I know the length of all three sides?

  

  You already know the base, so calculate the area past Heron'south formula. Then, substitute the values y'all know in the formula. Surface area=1/2 * base * height or height=2 * Area/base and find your reply.

• Question

  How practise I notice the height of a triangle?

  

  You need to know both the length of the base of the triangle and its expanse. Carve up the base into the surface area, and so double that.

• Question

  What is height of a triangle if the base is v and the two sides are 3?

  

  This is a trigonometry question. Draw the top from the obtuse angle to the "five" side. This forms ii right triangles inside the chief triangle, each of whose hypotenuses are "iii". The cosine of either of the original acute angles equals 2½÷3, or 0.833. Wait up that angle in a trig tabular array. Notice the sine of that angle, and multiply that by 3 to get the height.

• Question

  How do I discover the top of a triangle with the length of the three sides?

  

  Follow Method 3. "If you have all three sides, you'll utilise Heron'due south formula, and the formula for the surface area of a triangle." Utilise Heron's formula to make up one's mind the surface area of the triangle. Prepare the result equal to ane/2bh, and solve for h.

• Question

  How can I determine the tiptop of an isosceles triangle?

  

  Since the two opposite sides on an isosceles triangle are equal, you tin use trigonometry to figure out the tiptop. You tin find information technology by having a known angle and using SohCahToa. For example, say you had an bending connecting a side and a base that was 30 degrees and the sides of the triangle are 3 inches long and 5.196 for the base side. In order to notice the height, yous would need to prepare it up every bit this: S=o/h, Due south=sine, o=opposite (the height), h=hypotenuse (the side), S30=o/three considering it'due south the contrary divided by the three, you lot can multiply by the reciprocal on both sides and so the three gets cancelled on i side and the other is multiplied by 3, 3sin30=o and 3sin30=i.5=meridian.

• Question

  How exercise I find the elevation if the area and base of the quadrilateral are given?

  

  If it'south a regular quadrilateral, carve up the area by the base.

• Question

  Tin can I decide the base of operations of a triangle if I know its acme is eight feet?

  

  You would too need to know other information, such as the area or some of the sides or angles.

• Question

  What is the formula for determining the area of a triangle?

  

  One-half base times pinnacle.

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Article Summary X

If you know the base and expanse of the triangle, you can divide the base by 2, and so divide that by the area to notice the tiptop. To discover the height of an equilateral triangle, apply the Pythagorean Theorem, a^2 + b^2 = c^2. Cut the triangle in one-half downwards the middle, so that c is equal to the original side length, a equals half of the original side length, and b is the summit. Plug a and c into the equation, squaring both of them. Then subtract a^ii from c^2 and have the square root of the difference to find the summit. If you desire to learn how to calculate the area if yous only know the angles and sides, keep reading!

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