Answered

Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Get immediate and reliable solutions to your questions from a community of experienced experts on our Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

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

Sagot :

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:

[tex]c^2=a^2+b^2-2ab\cos (C)[/tex]

In our case:

[tex]c^2=105^2+60^2-2(105)(60)\cos (69.3)[/tex][tex]c^2=11025+3600-12600\cos (69.3)=14625-12600\cos (69.3)[/tex]

Taking the square root of both sides we get:

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

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

[tex]c=100.9[/tex]

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

View image MontrelT131889
View image MontrelT131889
Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.