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anonymous
 one year ago
Suppose you are standing on the edge of a canyon that is 400 meters high, where two sides of the canyon are at the same height and the walls of the canyon are perfectly vertical. The angle of depression to the bottom of the other side of the canyon is 14.3 degrees. Find the distance to the other side of the canyon. Ignore the height in the computations.
anonymous
 one year ago
Suppose you are standing on the edge of a canyon that is 400 meters high, where two sides of the canyon are at the same height and the walls of the canyon are perfectly vertical. The angle of depression to the bottom of the other side of the canyon is 14.3 degrees. Find the distance to the other side of the canyon. Ignore the height in the computations.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0basic tip: the angle of depression is the angle from the horizontal looking down at an object

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2dw:1437107516201:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0why are they right angles

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2dw:1437107592620:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Because the walls of the canyon are perfectly parallel and the same height.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Since the walls are perfectly vertical, they are both perfectly perpendicular to the ground. The ground is horizontal. Two lines perpendicular to the same line are parallel to each other.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Ok.You understand the drawing?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i get it now, i was confused on that part

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Ok. It means we have a rectangle. We are looking for x. dw:1437107821415:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2We can use trig of right triangles to find x.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2dw:1437107892862:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2The horizontal line at the top of the canyon, and the horizontal line at the floor of the canyon are parallel lines. We already know this because they are opposite sides of a rectangle. The line of sight is a transversal. This way we know the bottom right angle (marked above) measures 14.3 deg because the two 14.3 deg angles are alternate interior angles of parallel lines cut by a transversal.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Now we have a simple right triangle trig problem.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2We are looking for x. dw:1437108150647:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Do you remember the sine, cosine, and tangent ratios?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Do you use SOHCAHTOA to remember it?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Great. Here we have the 14.3 angle on the bottom right. For the 14.3 angle, is the x side the adjacent or the opposite leg?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and 400 is the opposite

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Great. That makes the 400 m side the opposite leg since the hypotenuse is unlabeled and we are not interested in it.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Yes, we use the tangent.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so basically I got 101.958

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2I don't get that.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Let me show you how just by logic and thinking you can tell that answer cannot be correct.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2You remember the good old 454590 triangle?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437108626021:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2If we had a 454590 triangle, the legs would be congruent, so x would also be 400 m, right? dw:1437108626987:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2dw:1437108699037:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so basically the distance to teh other side is 400 meters

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2No. I'm just explaining why 102 m cannot be correct. The answer has to be a number much larger than 400 m.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2In the 454590 case, the two legs would be 400 m. We don't have a 454590 case.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Since our bottom right angle is only 14.3 deg, the upper left angle is its complelement, so it's 75.7 deg.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0if possible could you draw your steps

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2dw:1437108865822:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Wit a 454590 triangle, x is the same as 400 m. Now see how our case more or less looks like above. As the top left angle gets larger and larger than 45 deg, the distance x also increases.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Since 75.7 is much larger than 45, x is much larger than 400 m.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Your last equation is incorrect bec you have adj/opp. The tan ratio is opp/adj. \(\tan \theta = \dfrac{opp}{adj} \) \(\tan 14.3^o = \dfrac{400~m}{x} \) \(x = \dfrac{400~m}{\tan 14.3^o}\)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2All you need to do is calculate x.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Don't forget the units.
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