Question

13. A tree casts a shadow of 30ft. The angle of elevation from the tip of the shadow to the top of the tree is 70 degrees. To the nearest foot, what is the height of the tree?

Answer 1

827

Answer 2

you have an angle...a side adjacent to that angle...and you want the side opposite that angle.

so which trig function uses Opposite and Adjacent?

Answer 3

@johnweldon1993 I think cos but I'm probably wrong haha

Answer 4

to remember the trig functions...remember

SOH CAH TOA

Sin = Opposite / Hypotenuse

Cos = Adjacent / Hypotenuse

Tan = Opposite / Adjacent

so which is it...?

Answer 5

Tan

Answer 6

Great....it is the tangent function

So

\[\tan = \frac{ Opposite }{ Adjacent }\]

You would plug in the values you have

\[\tan 70 = \frac{ Opposite }{ 30 }\]

and you want to solve for opposite...so what do you do...?

Answer 7

Uhm.. I'm not sure :/

Answer 8

No problem.....you would multiply both sides by 30 right?

when you multiply

\[\frac{ Opposite }{ 30 } * 30\]

the 30's cancel out

so now you would have

\[Opposite = \tan 70 * 30\]

So...what is the tan of 70 degrees?

Answer 9

I got 82.42 and a bunch of other numbers after that

Answer 10

ahhh skipped ahead a step :) lol

yes....now the question asks you "to the nearest foot" so what is 82.42 rounded to the nearest whole number?

Answer 11

Well I don't think I can round up so it would just be 82, right?

Answer 12

Or wait, maybe it could be 83

Answer 13

That is correct....*remember 82.49999999999999999999999999 is rounded to 82....

as soon as it hits 82.5...you would round up

so here you only have 82.42...so it would be...?

Answer 14

It would just be 82 :) I knew that you can only round up if the it's a 5 or more

Answer 15

There you go :)

Answer 16

Thank you! :)

Answer 17

anytime!