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- cherrilyn

trigonometry!!
a man standing 100ft away from a radio station observes that the angle of elevation to the base of the antenna mounted at the edge of the roof on top of the building is 25degrees. he also notices that the angle of elevation to the top of the antenna is 40degrees. approximate the height of the antenna on top of the building to the neraest foot.

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- cherrilyn

- schrodinger

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- cherrilyn

pleaaaaaaase help

- anonymous

It's about 37.28 ft

- cherrilyn

can you show me how to solve

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- anonymous

Do you want an explanation?

- anonymous

ok

- cherrilyn

thank you so much!

- anonymous

|dw:1327492056293:dw|

- anonymous

so, first, do you get the main picture?

- cherrilyn

yes

- anonymous

The angle between formed by the base of the radio station, the person, and the top is 40 degrees
and the angle formed between the person, base, and the bottom of the antennae is 25

- anonymous

This is where the sine rule comes in. We have the length of one side: 100m
We know every angle in the system. These conditions make the sine rule the best formula.

- cherrilyn

okay ... woops i was trying to use tangent

- anonymous

\[100\div \sin 65=x \div \sin 25\]

- anonymous

x is the length of the distance from the base of the network station to the antennae.

- anonymous

Haha, yeah, I do that a lot :P
so, x turns out to be 46.63 meters(about)

- anonymous

then, we need to find the whole distance from top to bottom. Once you get the whole distance and subtract 46.63, we get the part you're looking for

- anonymous

so, using the same equation...

- anonymous

\[100\div \sin 65=y \div \sin 40\]

- anonymous

The result of this is 83.91(about)

- anonymous

subtract the two and you've got 37.28 which is your answer XD

- anonymous

The explanation's kinda funky, but do you get it?

- cherrilyn

couldn't i just use tangent

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