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The spotter on the ground is standing beneath the safety net. What is his distance from the base of the platform, to the nearest meter?

Guest Oct 6, 2014

Best Answer 

 #2
avatar+80935 
+5

Notice that the angle that the platform makes with its support post is just 90 degrees. But 79 of those degrees have already been accounted for, so the remaining number of degrees in the apex angle of the triangle formed by the post, the distance the observer is from the post and the distance the observer is from the plattform = 90 - 79 = 11°

So we have a right triangle with a known angle - 11° - an adjacent side to that angle = 10m, and we're looking for the hypoteneuse (the distance the observer is from the bottom of the platform).

And the trig function that relates these is the cosine....so we have

cos(11°) = 10/h    where h = the hypoteneuse = the distance from the observer to the bottom of the platform

Rearanging gives us

h = 10/cos(11°) = about 10.187m ......rounded to the nearest meter, it would be 10m - but I don't really like that answer much, since the hypoteneuse is actually longer than any other side of the triangle!!!

 

CPhill  Oct 6, 2014
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2+0 Answers

 #1
avatar+354 
+5

First we find the size of the angle under the person on the platform. This is $${\mathtt{90}}{\mathtt{\,-\,}}{\mathtt{79}} = {\mathtt{11}}$$, so 11 degrees.

Next we use trigonomerty to find the length of the hypotenuse the triangle with side 10m and angle 11 and 90.

10m = Adjacent

Angle = 11

Hypotenuse = x

Cos(11)=10/x

x=10/Cos(11)

$${\mathtt{x}} = {\frac{{\mathtt{10}}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\mathtt{11}}^\circ\right)}}} \Rightarrow {\mathtt{x}} = {\mathtt{10.187\: \!166\: \!949\: \!548\: \!654\: \!9}}$$

rounding to the nearest meter, x=10m so the answer is 10m

(i think).

radio  Oct 6, 2014
 #2
avatar+80935 
+5
Best Answer

Notice that the angle that the platform makes with its support post is just 90 degrees. But 79 of those degrees have already been accounted for, so the remaining number of degrees in the apex angle of the triangle formed by the post, the distance the observer is from the post and the distance the observer is from the plattform = 90 - 79 = 11°

So we have a right triangle with a known angle - 11° - an adjacent side to that angle = 10m, and we're looking for the hypoteneuse (the distance the observer is from the bottom of the platform).

And the trig function that relates these is the cosine....so we have

cos(11°) = 10/h    where h = the hypoteneuse = the distance from the observer to the bottom of the platform

Rearanging gives us

h = 10/cos(11°) = about 10.187m ......rounded to the nearest meter, it would be 10m - but I don't really like that answer much, since the hypoteneuse is actually longer than any other side of the triangle!!!

 

CPhill  Oct 6, 2014

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