How do you understand this?

A woman looks down from a hot air balloon. She sees sheep below and measures the angle of depression as 35∘. If the sheep are 125 feet from where the woman is looking down from the balloon (hypotenuse), how high off the ground is the balloon?

a. 72 feet
b. 102 feet
c. 88 feet
d. 43 feet

Question

How do you understand this?

A woman looks down from a hot air balloon. She sees sheep below and measures the angle of depression as 35∘. If the sheep are 125 feet from where the woman is looking down from the balloon (hypotenuse), how high off the ground is the balloon?

a. 72 feet
b. 102 feet
c. 88 feet
d. 43 feet

jhonyy9 · Answer

try draw this case

mhanifa · Answer

To me "If the sheep are 125 feet from where the woman is looking down from the balloon (hypotenuse)" bit is confusing, it could be interpreted as vertical distance to the balloon, if the "hypotenuse" is not there

jhonyy9 · Answer

@extrinix any idea here ?

Extrinix · Answer

Well you have an angle, $35^\circ$ 
and you also have the hypotenous, $125ft$

and you need to find the height, which is the opposite to $35^\circ$

This is my thinking because it's not the angle shown from the balloon to the ground, it's the angle opposite of the height.

Extrinix · Answer

So it would be 
$sin(35^\circ)=\dfrac{x}{125}$

mhanifa · Answer

|dw:1623144960725:dw|

Extrinix · Answer

x is on the wrong side, the hypotenous is 125 and the length of the `opposite of 35°` is x

mhanifa · Answer

|dw:1623145391914:dw|

Extrinix · Answer

no, 125 is the `hypotenous` only

Extrinix · Answer

you would just leave the bottom side blank

Extrinix · Answer

leg*

mhanifa · Answer

"If the sheep are 125 feet from where the woman is looking down from the balloon" , suggests the horizontal leg is 125 ft, but adding the word  "hypotenuse" adds confusion

Extrinix · Answer

"if the sheep are 125 feet from where the woman is look down from the balloon (hypotenous)" Read further

Extrinix · Answer

It's saying that the length from the woman to the sheep is your hypotenous.

Extrinix · Answer

hypotenuse**

Autocorrect to hypotenous?? Ē

mhanifa · Answer

Thanks, this is my understanding of the problem but the thing is it leads to incorrect answer. 
And the correct answer choice given is c. 88 feet. 
This makes me to think the question is incorrect. And this is the word "hypotenuse"

mhanifa · Answer

And my answer choice is a. 72 feet, as you suggest too

Extrinix · Answer

Maybe it's,
$cos(90-35^\circ)=\dfrac{x}{125}$
??

Extrinix · Answer

No, because it would still be 72...

mhanifa · Answer

That comes from tan 35

Extrinix · Answer

Yeah I think either the correct answer choice is wrong or the question itself is wrong...

Extrinix · Answer

it also comes from cos 55

mhanifa · Answer

Thanks for your time.

Extrinix · Answer

We tried, but I'm guessing a messup in the question itself, not our calculations.

mhanifa · Answer

Yeah, the purpose of this question was to confirm this.

Extrinix · Answer

Ah, okay.