Answered

IDNLearn.com: Your one-stop platform for getting reliable answers to any question. Discover comprehensive answers to your questions from our community of knowledgeable experts.

Consult the figure. To find the length of the span of a proposed ski lift from A to B,
a surveyor measures the angle DAB to be 25° and then walks off a distance of
L = 1700 feet to C and measures the angle ACB to be 15°. What is the distance
from A to B?

Sagot :

MrRoyalidn

The figure is an illustration of laws of sines, and the distance from A to B is 2534 feet

How to determine the distance AB?

The given parameters are:

DAB = 25°

L = 1700

ACB = 15°

Start by calculating the measure of angles CAB and ABC

CAB = 180 - DAB

This gives

CAB = 180 - 25°

CAB = 155°

Also, we have:

ABC = 180 - CAB - ACB

ABC = 180 - 155 - 15

ABC = 10°

The length AB is then calculated using the following laws of sines

[tex]\frac{AB}{\sin(C)} = \frac{L}{\sin(B)}[/tex]

This gives

[tex]\frac{AB}{\sin(15)} = \frac{1700}{\sin(10)}[/tex]

Make AB the subject

[tex]AB = \frac{1700}{\sin(10)} *\sin(15)[/tex]

Evaluate

AB =  2533.8151116

Approximate

AB = 2534

Hence, the distance from A to B is 2534 feet

Read more about laws of sines at:

https://brainly.com/question/16955971

#SPJ1

Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and come back for more insightful information.