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1 year ago

Consult the figure. To find the length of the span of a proposed ski lift from A to B,

Mathematics

1 answer:

Natasha2012 [34]1 year ago

3 0

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

<h3>How to determine the distance AB?</h3>

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

$\frac{AB}{\sin(C)} = \frac{L}{\sin(B)}$

This gives

$\frac{AB}{\sin(15)} = \frac{1700}{\sin(10)}$

Make AB the subject

$AB = \frac{1700}{\sin(10)} *\sin(15)$

Evaluate

AB = 2533.8151116

Approximate

AB = 2534

Hence, the distance from A to B is 2534 feet

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