[SPLIT] You are looking up to the top of a 500ft tall tower

[TitanMath]

Would someone mind checking this problem for me though? I think i've done it right, but would like some reassurance is all.

You are looking up to the top of a 500ft tall tower at a 18.2 degree angle. How far from the base of the tower are you? (Round to 2 decimal places)

To start off I sketched a triangle ABC in which angle A was the 90 degree angle and angle C was the angle where the person was looking up. Then I labelled the sides d, e, and f, where d was 500 feet (the height of the building), e was the hypotenuse (not relavent to problem, I don't believe), and f was the distance between the person and building. So it was obvious the overall goal was to find the distance of f. So with that in mind, I set up my variables.

. . .A = 90 degree angle
. . .B = ?
. . .C = 18.2 degree angle

. . .d = 500
. . .e = ?
. . .f = ?

Then I figured out angle B with the following equation:

. . .180 - (90 + 18.2) = B
. . .180 - 108.2 = B
. . .71.8 = B

So with B figured out, I figured that I could use tan(B) to figure out the opposite side, f. So I set up the following equation:

. . .tan(71.8) = f / 500 <--- Multiply both sides by 500 giving....
. . .500(tan(71.8)) = f <----- Solve for tan(71.8) giving...
. . .500(3.04152) = f <---- Simplify...
. . .1520.76=f <---- Rounded answer

So the final variables were:

. . .A = 90 degrees
. . .B = 71.8 degrees
. . .C = 18.2 degrees

. . .d = 500 feet
. . .e = (irrelavent)
. . .f = 1520.76 feet

So the final answer would be "I am 1520.76 ft away from the base of the building" Correct?

Any check of this work would be greatly appreciated, thanks.

 

[arthur ohlsten]

Your approach is correct, and your answer is right

I would have done the problem slightly differently.

Tan 18.2 = 500/f
f= 500/tan 18.2 answer or
f=500 cot 18.2

check and see if this agrees with your answer
Arthur

 

[soroban]

Re: [SPLIT] You are looking up to the top of a 500ft tall to

Hello, TitanMath!

You are looking up to the top of a 500ft tall tower at a 18.2° angle.
How far from the base of the tower are you? (Round to 2 decimal places)

Your work is absolutely correct . . . Excellent!

You did, however, do more work than necessary.
It did not ask you to solve the entire triangle, just find side \(\displaystyle f.\)

As Arthur pointed out, the equation would be: \(\displaystyle \L\:\tan18.2^o \:=\:\frac{500}{f}\)

Then: \(\displaystyle \L\:f\:=\:\frac{500}{\tan18.2^o} \:=\:1520.75864\:\approx\:1520.76\) feet.