Question

More help with triangles...

Answer 1

A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed the angle of depression to the boat is 17°44'. When the boat stops, the angle of depression is 48°13' . The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round your answer to the hundredths place.

Answer 2

@satellite73 Would I use \[\tan \theta=\frac{ opposite }{ adjacent }\] to find what both of the triangle's adjacent side length are and then subtract?

Answer 3

yes

Answer 4

okay thank you

Answer 5

I would add one more decimal point to your numbers (to the nearest 1000th) and round to 100th after the calculation

Answer 6

or better yet, use all the decimals your calculator gives, and round at the very end

Answer 7

alright I will do that

Answer 8

@phi so when I round to the nearest foot the boat has traveled 160 ft, correct?

Answer 9

using
tan A = opp/adj
solve for adj :
adj = opp/tan A

opp is 200 ft

the longest side is 200/tan (17.733)= 625.426
did you get that for the longest side ?

Answer 10

would it not be adj=opp*tanA?

Answer 11

making the 17.73 degree side 63.9435?

Answer 12

\[ \tan A = \frac{o}{a} \]
multiply both sides by a
\[ a \tan A = \cancel a \frac{o}{\cancel a} \]
divide both sides by tan A
\[ \frac{a \cancel{\tan A}}{\cancel {\tan A}} = \frac{o} {\tan A} \]
\[ a = \frac{o} {\tan A} \]

Answer 13

ohh okay I see now so let me redo this really quick and get the right answer.

Answer 14

so it is 446.856 or is it 446.857

Answer 15

I am getting something very close but different

what did you get for the "closer leg"

Answer 16

625.5517883-178.6950542=446.8567341

Answer 17

\[a=\frac{ 200 }{ \tan(48.22) }=178.6950542\]

Answer 18

you are only using 2 decimals. you need more for better accuracy

Answer 19

so 48.216?

Answer 20

and 17.733

Answer 21

13/60 is 0.216666

if you want 3 decimals, (and we do -- if not more)
look at the 4th decimal. if 5 or bigger, round up
0.2166 has a 6 in the 4th place, so we use 0.217

Answer 22

44/60 is 0.73333
here the 4th decimal is 3, which is less than 5, so don't round up. we get 0.733

Answer 23

but you convert using a+(b*1/60)+(c*1/60*1/60)
so that would be 17+(44*1/60)=17.73333333
and 48+(13*1/60)=48.21666667

Answer 24

But with a calculator, you can keep all the numbers, or do the calculation on one line

** yes to your note. I was just showing the fractional part

Answer 25

okay so it would be A=625.4263468
and the other one would be A=178.7159794

Answer 26

which would make it 446.7103674 ft difference or, rounded to the hundreths place, 446.710 ft

Answer 27

hundreths is the first 2 decimals, so
446.71

but yes, that is the answer.

Answer 28

oh okay. thank you for your help.