Triangle Height Calculator with Degrees

This triangle height calculator helps you find the height of a triangle when you know two sides and the included angle. Whether you're a student studying geometry or a professional working with technical drawings, this tool provides quick and accurate results.

How to Use This Calculator

Using our triangle height calculator is simple. Follow these steps:

Enter the length of the first side of the triangle in the "First side" field.
Enter the length of the second side of the triangle in the "Second side" field.
Enter the included angle between these two sides in the "Included angle" field.
Click the "Calculate" button to see the height of the triangle.

The calculator will display the height of the triangle based on the values you entered. You can also reset the form to start over with new values.

Formula Explained

The height (h) of a triangle can be calculated using the formula:

h = (a × b × sin(γ)) / c

Where:

a is the length of the first side
b is the length of the second side
γ is the included angle between sides a and b (in degrees)
c is the length of the third side (which can be calculated using the Law of Cosines)

The formula first calculates the third side using the Law of Cosines, then uses this to find the height.

Worked Example

Let's say you have a triangle with sides of 5 units and 7 units, and the included angle is 45 degrees. Here's how to calculate the height:

Step 1: Calculate the third side (c)

Using the Law of Cosines:

c = √(a² + b² - 2ab × cos(γ))
c = √(5² + 7² - 2 × 5 × 7 × cos(45°))
c ≈ √(25 + 49 - 70 × 0.7071)
c ≈ √(74 - 49.497) ≈ √24.503 ≈ 4.95 units

Step 2: Calculate the height (h)

Using the height formula:

h = (a × b × sin(γ)) / c
h = (5 × 7 × sin(45°)) / 4.95
h ≈ (35 × 0.7071) / 4.95 ≈ 24.7475 / 4.95 ≈ 4.999 units

The height of the triangle is approximately 5 units.

Frequently Asked Questions

What is the formula for calculating triangle height with degrees?

The formula is h = (a × b × sin(γ)) / c, where a and b are the lengths of two sides, γ is the included angle in degrees, and c is the length of the third side calculated using the Law of Cosines.

Can I use this calculator for any type of triangle?

Yes, this calculator works for any triangle as long as you know two sides and the included angle. It's particularly useful for non-right-angled triangles.

What if I only know two angles and one side?

In that case, you would first need to find the missing sides using the Law of Sines before calculating the height. Our calculator handles this automatically when you provide two sides and the included angle.

Is the angle in degrees or radians?

The calculator uses degrees. Make sure to enter the angle in degrees, not radians.