Question

need some help with this yucky problem :)
from a ship offshore, the angle of elevation of a hill is 1.1 degrees. After the ship moves inland at 4.5 knots for 20 min, the angle of elevation is 1.4 degrees. How high is the hill? (1 knot = about 6080 feet per hour)
i found out that the boat with the 1,1 degree angle is 9120 ft from its second position with the 1.4 degree angle, but now im stuck :(

Answer 1

there might be a snappier way to do this but i came up with this one.
you know
\[\tan(1.1)=\frac{h}{x+9120}\] and also
\[\tan(1.4)=\frac{h}{x}\]

Answer 2

we can solve this equation for x and then for h we have
\[x\tan(1.4)=(x+9120)\tan(1.1)\]
\[x\tan(1.4)=x\tan(1.1)+9120\tan(1.1)\]
\[x\tan(1.4)-x\tan(1.1)=9120\tan(1.1)\]
\[x(\tan(1.4)-\tan(1.1))=9120\tan(1.1)\]
\[x=\frac{9120\tan(1.1)}{\tan(1.4)-\tan(1.1)}\]

Answer 3

i get
\[x=33428\] rounded. now
\[\tan(1.4)=\frac{h}{33428}\] so
\[h=33428\tan(1.4)=817\] rounded

Answer 4

i did not check the number 9120, i took your word for it

Answer 5

haha im think i got that part right, thanks! :D

Answer 6

yw