A tree is observed on the opposite bank of a river. At that point, the river is known to be 140 feet wide. The angle of elevation from a point 5 feet off the ground to the top of the tree is 20°. Find the height of the tree to the nearest foot.

Question

Florisalreadytaken · Answer

wrong

Florisalreadytaken · Answer

|dw:1622124318295:dw|height of tree is x right
angle of ELEVATION = $  20^\circ  $
river width = $ 140 \ ft   $

you are half right tho, we will be using TOA.
$$ tan 20^\circ =\frac{x-5}{140} $$
$$  0.364= =\frac{x-5}{140} $$
$$  50.96=x-5  $$
$$  x=55.96  $$
does that make sense?

Florisalreadytaken · Answer

so to it nearest foot it would be exactly $  56 feet $ : )

Concert24 · Answer

oh yeah sorry I'm stupid

TutoriaIs · Answer

Ah, that makes a lot more sense, thank you for the correction Flor.

Extrinix · Answer

|dw:1622124653258:dw|
Wouldn't it be +5 if you're trying to find the height?
Because it says the height `from` 5 feet above, meaning after you find x you add the 5 below to find the height.

If you understand what I'm saying.

Florisalreadytaken · Answer

what, no -- its your misconception

the height `from` 5 feet `above`

Extrinix · Answer

yea, which gives you the $20^\circ$, but it's asking for the height of it, and you're just measuring the tree from 5 feet above, which means you would need to add the 5 back to get the actual height.

Florisalreadytaken · Answer

do i really have to teach you how to read?

` A tree  ` is observed on the ` opposite bank of a river `. At that point, the ` river is known to be 140 feet wide ` . The `angle of elevation` from a point `5 feet off the ground`  to the top of the tree is `20°`. Find the height of the tree to the nearest foot.

you see now?

Extrinix · Answer

`Find the height of the tree to the nearest foot` it doesn't say whether or not it's from 5 feet above, but the `point at which it's viewed` is 5 feet `above`, so to find the `total height` of the tree you would have to add the 5 feet back.

Extrinix · Answer

|dw:1622125290059:dw|

Here maybe this will help you understand what I'm saying a little.

snowflake0531 · Answer

OH WAIT I SEE HOW YOU GUYS ARE UHHHH DIFFFERENT
EXTRINIX IS PUTTING X IS THE LENGTH, SO X IS JUST THE TOP HEIGHT
BUT FLOR IS PUTTING THE X LENGTH AS THE ENTIRE THING

Extrinix · Answer

the angle value would change if he did the WHOLE thing.

snowflake0531 · Answer

but he did x-5

snowflake0531 · Answer

x-5 is your x

Extrinix · Answer

yeah, but the angle is for 5 feet above, not for ground level 0.

snowflake0531 · Answer

idk i just noticed the x differences ¯\_(ツ)_/¯

Concert24 · Answer

so I'm putting in 56 as my answer is it correct?

snowflake0531 · Answer

yk, flor is right, he did add the 5, it's cuz he put x-5, so at the end he still adds 5

Extrinix · Answer

The angle would be the same still.

Extrinix · Answer

|dw:1622125807506:dw|

snowflake0531 · Answer

yes, it is the same, you told him to add 5, but he already did that

snowflake0531 · Answer

no, x-5, is your x, so putting it in that equation, it's the same, just imagine the x-5 as your x, and then at the end dadding 5 again

Extrinix · Answer

*shrugs* well

snowflake0531 · Answer

@snowflake0531 wrote:

no, x-5, is your x, so putting it in that equation, it's the same, just imagine the x-5 as your x, and then at the end dadding 5 again

*adding

Concert24 · Answer

so is 56 the correct answer?

snowflake0531 · Answer

ye