Question

This word problem has got me completely stuck:

A ship is just offshore of New York City. A sighting is taken of the Statue of Liberty, which is about 305 feet tall. If the angle of elevation to the top of the statue is 22°, how far is the ship from the base of the statue?

Answer 1

It helps to draw a picture..

Answer 2

I would advice drawing a diagram. The 305 feet tall refers to the opposite side of a right-angled triangle. Which angle is the angle of elevation? What side of the triangle are you trying to find if you want to know how far the ship is from the base of the statue?

Answer 3

ive tried 305cos22 because i thought i was looking for the adjacent side of the angle of elevation and my hyp. is 305 and just cross multiply but I keep getting the wrong answer.

Answer 4

The 305 feet refers to the \(opposite\) side of the the triangle, and not the hypotenuse. How would you go about solving it with this piece of information?

Answer 5

Here's my terrible rendition.

Answer 6

i agree with polpak's drawing

Answer 7

so tan which is opp/adj
and then tan22= 305/x

Answer 8

\[d=305 \text{ Cot}[22 {}^{\circ}]\]\[d=755 \text{ feet}\]

Answer 9

oh oh cot! i meant

Answer 10

you can do tan

Answer 11

solve for x in your equation

Answer 12

okay, thank you!! (:

Answer 13

we need a picture that is 1:1 scaled ;)

Answer 14

\[h(cos\ 22^\circ) = x\]\[h(sin\ 22^\circ) = 305\]\[\implies \frac{x}{305} = \frac{(cos\ 22^\circ) }{(sin\ 22^\circ) }\]\[\implies x =305\frac{(cos\ 22^\circ) }{(sin\ 22^\circ) } \]

Answer 15

or x=305cot(22)
or x=305/tan(22)
all have same meaning

Answer 16

bah, shoulda used r. h is ambiguous.. I meant it to be hypotenuse but it could be interpreted wrongly as height.

Answer 17

Yeah, but I hate trying to remember all that other nonsense, cot, etc. easier just to use sines and cosines usually.

Answer 18

cot=adjacent/opposite
tan= opposite/adjacent

Answer 19

sin=opp/hyp
cos=adj/hyp

tan=sin/cos=opp/adj

Answer 20

Yeah I can figure it out, but I hate trying to remember all of those relationships.

Answer 21

Easier for me to remember the basic one, and derive the rest as needed.

Answer 22

but i suppose we only really need sin and cos

Answer 23

all the trig relations can be written in terms of sine and cosine

Answer 24

tan(22) = 305/d

d = 305/tan(22) is what i get

Answer 25

thanks for using derive right amistre i mean polpak

Answer 26

its wait i got too :)