Question

Look at this triangle.
B В
13 cm
8 cm
Work out length BC.

Answer 1

13² = 169
8² = 64

169 - 64 = 105

Square root of 105 = 10.247cm

Answer 2

The length of BC is the square root of 105. If you want a numerical approximation: BC≈√105≈10.25

To find the length of side BC in the given triangle, you can use the Pythagorean Theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides

Let's denote the sides of the triangle as follows:

AB (hypotenuse) = 13 cm

AC = 8 cm

BC (the side we want to find)

The Pythagorean Theorem is given by:

ᴬᴮ²⁻ᴬᶜ²⁺ᴬᴮ²

Now, substitute the given values into the equation and solve for BC:

¹³²⁻⁸²⁺ ᴮᶜ²

169-64+ ᴮᶜ²

Subtract 64 from both sides:

. ᴮᶜ²+=169-64

ᴮᶜ² - 105

Now, take the square root of both sides to solve for BC:

BC-√105

So, the length of BC is the square root of 105. If you want a numerical approximation:

BC≈√105≈10.25