SOLUTION: Jack is on one side of a 150ft wide canyon and Jill is on the other. Jack and Jill can both see the trail guide at an angle of depression of 50 degrees. How far are they from the t

Question 1082173: Jack is on one side of a 150ft wide canyon and Jill is on the other. Jack and Jill can both see the trail guide at an angle of depression of 50 degrees. How far are they from the trail guide?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
they're on both ends of the canyon and they both see the guide at a 50 degree angle.

they and the guide form an isosceles triangle.

the perpendicular from the guide to their level splits the distance between them in half.

2 right triangle are formed.

call the triangle ABC.
one end of the canyon is A.
the other end of the canyon is B
the guide is C.
the perpendicular from the guide to their level is D.
D splits AB in half.
2 right triangles are formed.
ADC and BDC are the triangles.
angles DAC and DBC are each 50 degrees.
the distance from the guide to each is the hypotenuse of the right triangles ADC and BDC.
cos(50) = opp / hyp
the distance from A to D and B to D is 75 feet.
cos(50) = opp / hyp = 75 / hyp
solve for hyp to get hyp = 75 / cos(50).
result is hyp = 116.679287 feet.
that's the distance from each to the guide.
the picture is shown below:
$$$

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