from the top of a tower 63.2 feet high, the angles of depression of two objects situated in the same horizontal line with the base of the tower, and on the same side of the tower, are 31.16 degree' and 46.28 degree' respectively. Find the distance between two objects.

Question

qweqeeqw · Answer

can you draw it? thankyou

qweqeeqw · Answer

okay no problem thankyou for the response

Extrinix · Answer

I see something I did wrong, give me a moment.

Extrinix · Answer

so, for this question we are given the height, which we can identify as the `adjacent` side to the angles listed

now we need to find the `opposite` side, look at this list:

sin = $\dfrac{o}{h}$
cos = $\dfrac{a}{h}$
tan = $\dfrac{o}{a}$

now find the one needed, `tan` and create the equation
$tan(31.16^\circ)=\dfrac{x}{63.2}$
$~~~~\downarrow~~~~$
$x=63.2tan(31.16^\circ)$
gives you: $\approx$ 38.2

now, thats the shortest distance from the tower
now we find the 46.28 angle, using `tan` as well

$tan(46.28^\circ)=\dfrac{x}{63.2}$
again, solve it
$x=63.2tan(46.28^\circ)$
it gives you: $\approx$ 66.1

now, to find the distance `from` each other, subtract the higher number from the lower number

$66.1-38.2$

which gives you: $27.9$

that is your distance between the two angles.

Extrinix · Answer

I did hypotenous instead of opposite, my mistake.

qweqeeqw · Answer

Thats okay thankyou so much

Extrinix · Answer

Eres bienvenido.

jhonyy9 · Answer

maybe a good help an image about this case

Extrinix · Answer

I'm on mobile so I can't right now, would you mind jhonyy?

Florisalreadytaken · Answer

attachment

Extrinix · Answer

Thank you, Flor

qweqeeqw · Answer

thankyou guys

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