Question

The figure shows the location of three points around a lake. The length of the lake, BC, is also shown.

(The figure is not drawn to scale.)

Which of the following choices is closest to the distance (in miles) between points A and B?


3.16 miles
3.46 miles
4.47 miles
490 miles

Answer 1

`a^2 + b^2 = c^2\\\\ 4^2 +AB^2 = 6^2 \\\\AB^2 = 6^2 -4^2\\\\AB^2 = 36-16\\\\AB^2 = 20\\\\AB = √(20) \\\\AB = \boxed {4.47}`

Answer 2

The distance between points A and B is 4.47 miles.

Explanation:

Pythagoras' theorem-

It states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Here, AC is the hypotenuse and AB and BC are the two legs.

Applying the Pythagoras' theorem,

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

`\Rightarrow AB^2=AC^2-BC^2`

`\Rightarrow AB=√(AC^2-BC^2)`

`\Rightarrow AB=√(6^2-4^2)=√(36-16)=√(20)=4.47`