A television antenna 20 m high stands top of a house which 12 m high. At what distance from the base of the house will the antenna and the house subtend equal angle?
A. 24 m* B. 15 m C. 31 D. 28 m
the answer should be 24

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- anonymous

- schrodinger

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- welshfella

|dw:1443354484410:dw|

- welshfella

so you need to find D when x = y right?

- welshfella

r u there?

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## More answers

- radar

I'm here, but it is not my problem @welshfella, was hoping you would provide some more steps (for my own edification lol).

- anonymous

i have tried to solve it but i cant get 24m

- anonymous

we have the same drawing but still i cant get the answer

- welshfella

lol ok
well i think we can use the double angle formula.
write y for x:-
so
tan 2y = 2 tan y
--------
1 - tan^2 y
and tan y 2y = 32/D and tan y = 12 / D

- welshfella

* that's tan 2y = 32 / D

- anonymous

what should i do next?

- welshfella

plug tan 2y = 32/D and tan y = 12/D into the above identity and solve for D

- IrishBoy123

@welshfella big fat Celtic Congrats, mate!!!

- welshfella

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- welshfella

HaHa Thanks Irish boy. We beat the English!!!!

- welshfella

@Jluz - can you solve that one for D?

- anonymous

i used my calcu shift solve but it doesnt result in to 24m

- radar

Yes is does, thanks @welshfella

- anonymous

@radar i cant get it my answer is 12.38

- welshfella

yea I get the same as you JLuz
Maybe i made a mistake somewhere....

- radar

|dw:1443355873893:dw| Do you follow this far @JLuz

- anonymous

yes

- radar

|dw:1443355996631:dw| How about to this?

- welshfella

yea it does work out to 24

- radar

|dw:1443356181782:dw| and then to this?

- welshfella

gotta go
ul leave you in capable hands of radar

- radar

Can you take it to "24" ?

- anonymous

i wil solve

- radar

Good As you see, I just used "cross multiplication" of the fraction.

- anonymous

wow yea

- radar

Good luck with your studies.

- anonymous

is results to 24

- anonymous

i have a question

- anonymous

why does she uses double angle formula??

- radar

Go ahead, but I think @welshfella has left, he had the incite for the solution.

- radar

Because the angle to the top of the antenna is equal to the sum of the two equal angles to the top of the house and the angle from the top of the house to the top of the antenna. In the drawing the big angle is equal to the sum of X and Y and we are told that they are equal .......... hence "double angle"

- radar

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- radar

I was messing around trying to use the law of sines and wasn't getting anywhere, I think that double angle approach was a good idea.

- anonymous

i was trying to analyze your explanation haha

- anonymous

nosebleed haha

- radar

The use of the double angle identity was a wise choice. You will run into that identity in Trig' maybe you already have studied the trigometric identities.

- anonymous

ok radar thank you for your big help

- anonymous

it is a big help in my studies

- radar

Good luck

- radar

I think you will do well, because you knew what the answer was, but you needed to know "how" or verify that it was indeed a correct answer, that is a good trait.

- anonymous

as well as to @welshfella

- anonymous

thanks @welshfella

- welshfella

yw

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