The pilot of a small boat measures and determines that the angle of elevation of the the top of a lighthouse is 19°. The Lighthouse reaches 21m above sea level. Find the distance between the boat and the lighthouse.
I don't know which function to use because when I draw the right angle the problem doesn't tell you which is x and which is y.
2007-09-24 19:58:29 · 5 answers · asked by SUPERMAN 2 in Science & Mathematics ➔ Mathematics
With the following statement you gave, it is easier to associate your "x" be the horizontal which is going to be the distance of the boat from the lighthouse and your "y" be the vertical part which is going to be the height of your lighthouse itself.
So using the tangent formula:
tan (19°) = y / x substituting the values for the variables
tan (19°) = 21 / x isolating variables on one side
x = 21 / tan (19°) perform operation
x = 60.99 meters
so the distance between the baot and the lighthouse is 60.99 meters.
2007-09-24 21:06:31 · answer #1 · answered by hayaku_raven22 2 · 0⤊ 0⤋
try this if it will work for you:
don't confuse yourself with all those x's and y's, just remember this mnemonic:
SOH CAH TOA ---> pronounced sokatowa
SOH
sin = opposite / hypotenuse
CAH
cos = adjacent / hypotenuse
TOA
tan = opposite / adjacent
*** I believed you have drawn the figure for the problem. you have the 19°, the 21m height of lighthouse, and an unknown distance between boat and lighthouse. Based from that drawing determine w/c side is opposite, adjacent, and hypotenuse. Let's make the 19° as the reference point. First, the hypotenuse is the longest side (this is the line connecting the boat to the tip of the lighthouse). Second, the opposite is the side opposite the 19° angle ( in this case, the height of the tower w/c is 21m). Lastly, the adjacent is the remaining side which is the distance we want to know)... just to give you an idea, adjacent side is that side which is used by the known angle, 19° in this example, aside from the hypotenuse.
So, you know the angle (19°), you know the opposite side (21m) but you dont know the adjacent... from this given quantities, tangent is the best trigo function to use:
tan = opposite / adjacent
tan 19° = 21 / adjacent
adjacent = 21 / tan 19°
adjacent = (** solve on, use your calculator to finish it up)
2007-09-25 03:35:31 · answer #2 · answered by paranoia 2 · 0⤊ 0⤋
hi!
i dont have a scientific calculator right now
but this could help
x= the distance
y= 21 m
by using trigo function:
tan 19 = 21/x
x= 21/ arc tan 19
x= _________just press it on your calculator
2007-09-25 03:33:06 · answer #3 · answered by Niño C 1 · 0⤊ 0⤋
tan19° = 21 m / distance
2007-09-25 03:15:35 · answer #4 · answered by Helmut 7 · 0⤊ 0⤋
It is up to you to assign which is which.
Your best bet would be to use the tangent function. :)
2007-09-25 03:07:23 · answer #5 · answered by Pilosopong Tasyo 2 · 0⤊ 0⤋