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# find the length of track???

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The Duquesne Incline is a cable car in Pittsburg, Pennsylvania, which transports passengers up and down a mountain. The track used by the cable car has an angle of elevation of 30 degrees. The angle of elevation to the top of the track from a point that is horizontally 100 feet from the base of the track is about 26.8 degrees. Find the length of the track.

Mar 6, 2018

#2
+68
+2

The easiest thing to do in this situation is to draw a picture.

Then we label the information.

What we can do is use the 100 feet as a line. So I'm going to extend the bottom line to make it just under the top point. Then I'm going to move the bottom line down. The new angles are 60 and 30 degrees.

Now we can use SOH CAH TOA to find the hypotenuse. In this case, we would use cosine, since we have 100ft as the adjacent side and we're trying to find the hypotenuse.

The rest is using trig.

$$cos(30°)=\frac{100}{x}$$

$$\frac{\sqrt{3}}{2}=\frac{100}{x}$$

$$200=\sqrt{3}x$$

$$x=\frac{200}{\sqrt{3}}$$

$$x= 115.4701 ft$$

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Mar 6, 2018
edited by CoopTheDupe  Mar 6, 2018

#1
+18329
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tan 26.8 = opposite/ adjacent  =  opposite/100        solve for opposite to get HEIGHT  (50.51 ft)

then   sin 30 = opposite/hyp  to get hyp...the lenght of the track.    101.02 ft

Mar 6, 2018
edited by ElectricPavlov  Mar 6, 2018
#2
+68
+2

The easiest thing to do in this situation is to draw a picture.

Then we label the information.

What we can do is use the 100 feet as a line. So I'm going to extend the bottom line to make it just under the top point. Then I'm going to move the bottom line down. The new angles are 60 and 30 degrees.

Now we can use SOH CAH TOA to find the hypotenuse. In this case, we would use cosine, since we have 100ft as the adjacent side and we're trying to find the hypotenuse.

The rest is using trig.

$$cos(30°)=\frac{100}{x}$$

$$\frac{\sqrt{3}}{2}=\frac{100}{x}$$

$$200=\sqrt{3}x$$

$$x=\frac{200}{\sqrt{3}}$$

$$x= 115.4701 ft$$

CoopTheDupe Mar 6, 2018
edited by CoopTheDupe  Mar 6, 2018