Question

Two points, A and B, are on opposite sides of a building. A surveyor chooses a third point, C, 60 yd from B and 105 yd from A, with angle ACB measuring 69.3 . How far apart are A and B (to the nearest yard)?A. 101 yardsB. 110 yardsC. 119 yardsD. 128 yards

Answer 1

Let's draw a diagram of this problem:

This triangle can be seen as follows:

We can use the Law of Cosines to find the length of side c, since we know the measure of angle C:

`c^2=a^2+b^2-2ab\cos (C)`

In our case:

`c^2=105^2+60^2-2(105)(60)\cos (69.3)`
`c^2=11025+3600-12600\cos (69.3)=14625-12600\cos (69.3)`

Taking the square root of both sides we get:

`c=\sqrt[]{14625-12600\cos (69.3)}`

which, using a calculator or online resource to calculate the right side of the equation will give us:

`c=100.9`

To the nearest yard, A and B are 101 yards apart, so option A. is correct.