Q&A for How to Find the Height of a Triangle

H = height, S = side, A = area, B = base. You know that each angle is 60 degrees because it is an equilateral triangle. If you look at one of the triangle halves, H/S = sin 60 degrees because S is the longest side (the hypotenuse) and H is across from the 60 degree angle, so now you can find S. The base of the triangle is S because all the sides are the same, so B = S. Using A = (1/2)*BH, you get A = (1/2)*SH, which you can now find.

Look up the tangent of the angle in a trigonometry table. Multiply the tangent by the length of the base.

You already know the base, so calculate the area by Heron's formula. Then, substitute the values you know in the formula. Area=1/2 * base * height or height=2 * Area/base and find your answer.

You need to know both the length of the base of the triangle and its area. Divide the base into the area, then double that.

This is a trigonometry question. Draw the height from the obtuse angle to the "5" side. This forms two right triangles inside the main triangle, each of whose hypotenuses are "3". The cosine of either of the original acute angles equals 2½÷3, or 0.833. Look up that angle in a trig table. Find the sine of that angle, and multiply that by 3 to get the height.

Follow Method 3. "If you have all three sides, you'll use Heron's formula, and the formula for the area of a triangle." Use Heron's formula to determine the area of the triangle. Set the result equal to 1/2bh, and solve for h.

Since the two opposite sides on an isosceles triangle are equal, you can use trigonometry to figure out the height. You can find it by having a known angle and using SohCahToa. For example, say you had an angle 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 find the height, you would need to set it up as this: S=o/h, S=sine, o=opposite (the height), h=hypotenuse (the side), S30=o/3 because it's the opposite divided by the three, you can multiply by the reciprocal on both sides so the three gets cancelled on one side and the other is multiplied by 3, 3sin30=o and 3sin30=1.5=height.

If it's a regular quadrilateral, divide the area by the base.

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

One-half base times height.

Assuming a Side-Angle-Side relationship, that would be the two sides multiplied by 1/2, then multiplied by the sine of the angle.

You multiply all of the numbers and divide by two, since it is a triangle.

You can't.

Mark the two sides and draw the appropriate line between them. Once you've done that, just calculate as normal.

You would also have to know the base.

Consider the triangle formed by the known side, the known angle, and the height opposite the known angle. Write a trigonometric equation for the tangent of the known angle, making use of the known side and the height. Solve for the height.

Make a line straight down from the top of the triangle, thus forming a right triangle. Then use A squared + B squared = C squared (aka the Pythagorean Theorem).

You have to know the height, too.

First multiply the area by 2.3. Then find the square root of that number. That's the length of a side.

The usual formula is one-half the base multiplied by the height.

No. The triangle is ambiguous and has no set shape, and therefore no discernible area.

You don't have enough information to do that.

You don't have enough information to find the height.

Look up the tangent of 56°, then multiply it by 100 ft.

You would divide the base into 2 equal parts, so half of 6 is 3. Then you know you have a 30-60-90 right triangle, with a hypotenuse of 6 and a base of 3. Since this triangle has side lengths of 2x, x, and x(sqrt3), you know that 6 is 2x and 3 is x. Then you know the height is 3(sqrt3).

This is called a "30-60-90 triangle" (those are its angles), and the sides of it are in the ratio of 1 : √3 : 2. The "2" corresponds to the hypotenuse (the longest side), which is given as 7 cm. We can set up two proportions to find the legs of the triangle: 2 / 7 = 1 / x, and 2 / 7 = √3 / y, where x and y are the legs. By cross-multiplying we find that x = 3.5 cm and y = 7.5√3 cm. We'll call the longer leg the base of the triangle and the shorter leg the height. (It could also be reversed.) The area is (½)(base)(height) = (½)(7.5√3)(3.5) = 22.7 sq cm.

A = 40 = (base)(height) / 2 = (5)(3x - 7) / 2 = (15x - 35) / 2. Then 80 = 15x - 35, and 115 = 15x. So x = 7.67.

It can't be done. You need more information.

No, there is not. Heron's Formula is very helpful though, and it isn't as tedious as it seems. Just practice and soon it will become easier.

Sides a, b, c are known. The semi-perimeter, s = (a+b+c)/2. Area of Triangle = sqrt[s(s-a)(s-b)(s-c)] and Area of Triangle = b * h / 2. Therefore : b * h / 2 = sqrt[s(s-a)(s-b)(s-c)] h = 2 * sqrt[s(s-a)(s-b)(s-c)] / b