Question

An equilateral triangle with side length 3 cm is shown in the diagram, work out the height of the triangle.

Give your answer rounded to 1 DP.

Answer 1

The height of an equilateral triangle can be found using the Pythagorean theorem by treating it as a 30-60-90 triangle. In a 30-60-90 triangle, the ratio of the side lengths is 1:√3:2. In this case, the side length of 3 cm is the shorter leg, so the height (the longer leg) is 3√3 cm. Rounding to 1 decimal place, the height is approximately 5.1 cm.