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Math 175 , please i need help

Find the height of a tree if the angle of elevation of its top changes from 20 to 40 as the observer advances 75 feet toward its base ?

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Again, a picture would help. Ok, draw a horiz. line, with the left endpoint called A and the right called B. From B, draw a line straight up to endpoint C. Then, draw from C back to A. This is a right triangle ABC, with the right angle at point B.

Now, draw point (D) on line AB - say about 1/3 of the way along it. Draw a line from D to C. This creates another right triangle DBC inside of triangle ABC. From your problem: angle CAB is 20 deg, angle CDB is 40 deg and the length of AD is 75 feet.

You need to find the length of side CB, the height of your tree. You will use the tangent function (tan = opp/adj), and substitution with two equations.

In triangle DBC, tan 40 = CB/DB. So, DB = CB/tan 40.
In triangle ABC, tan 20 = CB/AB = CB/(75 + DB). Solving for CB:
CB = tan 20 (75 + DB). Substituting DB from above:
CB = tan 20 (75 + [CB/tan 40]) Distributing the tan 20:
CB = tan 20 (75) + CB (tan 20/tan 40) Simplifying:
CB (1 - [tan 20/tan 40]) = tan 20 (75) Dividing:
CB = [tan 20 (75)/(1 - [tan 20/tan 40]]

Since tan 20 and tan 40 are simple numbers, you can calculate CB, the height of your tree. Good luck!