SOLUTION: Hey! I am having difficulty answering this question, may you please help me? "Trish is working out the height of a communications tower. From point A she takes a sighting of the

Question 866764: Hey! I am having difficulty answering this question, may you please help me?
"Trish is working out the height of a communications tower. From point A she takes a sighting of the top of the tower (30 degrees). She then moves 100 metres to point B and takes another sighting (85 degrees). Calculate the height of the tower, to the nearest metre."
I really appreciate your help. Thank you!
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
look at the following diagram:
$$$

tan(30) = x / (100 + y)
solve for x to get:
x = 100*tan(30) + y*tan(30)

tan(85) = x / y
solve for x to get:
x = y*tan(85)

since x is equal to both expressions on the right of each equation, then you can set the expressions equal to each other to get:

100*tan(30) + y*tan(30) = y*tan(85)

solve this equation for y to get:

y = 100 * tan(30) / (tan(85) - tan(30))

solve for y to get:

y = 5.319875801

in the equation of x = y*tan(85), replace y with 5.319875801 to get:

x = 5.319875801 * tan(85)

solve for x to get:

x = 60.80645864

that's your answer.

i'm assuming you know how to solve equations for x and y.
if you're having trouble with that, let me know and i'll send you more details on solving these equations.

to confirm your solution is correct, replace x with 60.80645864 and replace y with 5.319875801 and solve for tan(30) and tan(85).

tan(30) should be equal to .577350269
tan(85) should be equal to 11.43005230

these are the results when you look for tan(30) and tan(85) in your calculator.

from your problem, the equation for tan(30) should be:
tan(30) = x / (100 + y)

from your problem, the equation for tan(85) should be:
tan(85) = x / y
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