Question #6f115

1 Answer
Oct 24, 2017

#p ~~ 51.4 "ft"#

Explanation:

See the diagram below.

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In the diagram, #alpha# represents the angle the pole makes with the ground, while point #P# marks the edge of the shadow on the ground.

From inspection, we can see that the angles #alpha#, #beta#, and #55^o# must all sum to #180^o#. Furthermore, since the pole makes an angle of #7^o# to the vertical, we know that #alpha + 7^o = 90^o#, and thus #alpha = 83^o#.

This means that we can calculate #beta#:

#alpha + beta + 55^o = 180^o #

#83^o + beta + 55^o = 180^o #

#beta = 42^o#

Since we now have #/_P#, #beta#, and #b#, and we are looking for #p#, the Law of Sines can be helpful here:

#sin P/p = sin beta/b#

#sin 55^o/p = sin 42^o/42#

#(42*sin 55^o)/(sin 42^o) = p#

#p ~~ 51.4 "ft"#