Question

em E < Back to task Calculator allowed This is a new version of the question. Make sure you start new workings. 12 Use Pythagoras' theorem to work out the height of the equilateral triangle below. Give your answer in centimetres (cm) to 1 d.p. 20 Bookwork code: N66 Search 18 cm 18 cm 18 cm Not drawn accurately Watch video 19,585 XP Answer > Ca​

Answer 1

To find the height of an equilateral triangle, we can use the Pythagorean theorem. In an equilateral triangle, all sides are equal in length, and the height divides the triangle into two right-angled triangles.

Let's denote the height of the equilateral triangle as 'h' and the length of one side as 's'.

Using the Pythagorean theorem, we can write:

s^2 = h^2 + (s/2)^2

Since all sides of the equilateral triangle are 18 cm, we can substitute 's' with 18 in the equation:

18^2 = h^2 + (18/2)^2

324 = h^2 + 81

h^2 = 324 - 81

h^2 = 243

Taking the square root of both sides, we get:

h = √243

Calculating the square root of 243, we find:

h ≈ 15.588 cm

Therefore, the height of the equilateral triangle is approximately 15.588 cm (rounded to 1 decimal place).