Question

Help. I just need to know the length of the AC side

Answer 1

`AC=√(105)\approx10.25\text{cm}`

Explanation:

this is a right triangle, and we are given the hypotenuse as 11 and one side as 4. we are to find AC.

recall for right triangles, we can use the Pythagorean theorem, which states that
`a^2+b^2=c^2`, where a and b are the shorter sides and c is the hypotenuse.

so, we substitute the values:
`4^2+AC^2=11^2`. then, expand and simplify.

`16+AC^2=121\to AC^2=121-16\to AC^2=105`

finally, take the square root of both sides.

`\therefore AC=√(105)\approx10.25`. ignore the negative answer since length can't be negative.

Answer 2

`\sf AC = √(105) \textsf{ or } 10.25` centimeters

Explanation:

Given:

In ∆ ABC

• C is a right angle
• BC = 4cm
• AB = 11cm

To find:

• AC = ?

Solution:

In a right-angled triangle, the Pythagorean theorem states that the square of the length of the hypotenuse (
`\sf AB`) is equal to the sum of the squares of the lengths of the other two sides (
`\sf AC` and
`\sf BC`).

The Pythagorean theorem is given by:

`\sf AB^2 = AC^2 + BC^2`

Given that
`\sf AB = 11 \, \text{cm}` and
`\sf BC = 4 \, \text{cm}`, you can substitute these values into the equation and solve for
`\sf AC`:

`\sf 11^2 = AC^2 + 4^2`

`\sf 121 = AC^2 + 16`

Now, subtract 16 from both sides:

`\sf AC^2 = 105`

Take the square root of both sides to find
`\sf AC`:

`\sf AC = √(105)`

`\sf AC \approx 10.24695077 \, \text{cm}`

`\sf AC \approx 10.25 \, \text{cm ( in 2 d.p.)}`

So, the length of
`\sf AC` is
`\sf √(105) \textsf{ or } 10.25` centimeters.