Answered

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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 :

MrRoyal

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

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