At the zoo, an 8 m tall high-security fence is leaning at an angle of 6 degree to the vertical. To prevent the fence from toppling over, a support pole.....
...must be placed inside the animal enclosure that attaches 2m from the top of the fence at an angle of 50 degree with the ground. How long does the pole has to be, to the nearest tenth of a meter(rounding to one decimal place)? include the diagram.
We assume the fence leans in towards the enclosure.
(1) The angle the fence makes with the ground is 90-6=84 degrees. The angle the support pole makes with the ground is given as 50 degrees. The angle where the pole meets the fence is 46 degrees.(The angle sum of a triangle is 180)
(2) The length of the fence is 6m, as the pole meets the fence 2m from the top.
(3) Applying the law of sines (letting the length of the pole be p) we have `6/(sin 50)=p/(sin84)` or `p=(6sin84)/(sin50)~~7.8` .
Thus the length of the pole is approximately 7.8 meters.