Question

Will FAN and MEDAL

A plane is located at C on the diagram. There are two towers located at A and B. The distance between the towers is 7,600 feet, and the angles of elevation are given.




a. Find BC, the distance from Tower 2 to the plane, to the nearest foot.
b. Find CD, the height of the plane from the ground, to the nearest foot.

Answer 1

@jim_thompson5910 @Hero @satellite73 @ganeshie8

Answer 2

@mathstudent55

Answer 3

its easy .. u just need to revise the basic sine and cosine functions

Answer 4

because u dnt knw the full lenght of base .. u will be two equations in 1 variable .. so at the end u will solve them and give the results ..

Answer 5

hmm, alright

Answer 6

?

Answer 7

Oops I forgot what we were solving for!

Anyways... first we take the sine of the two angles we are given...

so

sin 16 = CD/AD

and sin24=CD/BD

Answer 8

And we can also relate AD and BD because AD-BD=7600ft (check graph to see how this makes sense)

Answer 9

Now... if we can find BD (which you can by using the equations I posted) we will be able to solve for BC

Answer 10

So do you have any ideas how to solve for BD?

Answer 11

\[\frac{ BC }{\sin16 } =\frac{ 7,600 }{ \sin8 }\]

Answer 12

maybe?

Answer 13

hmm let me just check what you did there

Answer 14

yes you are correct! And that way is much faster than what I was doing.

Now that you have BC, you will probably notice that you can use sin24 to find the CD

Answer 15

Im not so sure, the equation is as far as I got

Answer 16

Do you know how to solve for BC?

Answer 17

yes, I got 122.7 ft

Answer 18

well at least thats what i got

Answer 19

@timely

Answer 20

Sorry! I had a problem with my internet connection.

122.7 feet seems very very low for length BC

Answer 21

\[\frac{ BC }{ \sin16 }=\frac{ 7600 }{ \sin8 }\]

isolate BC by multiplying both sides by sin16

\[(\sin16)\frac{ BC }{ \sin16 }=\frac{ 7600 }{ \sin8 }(\sin16)\]

as you can see... sin16 cancels out on left side

\[BC =\frac{ 7600 }{ \sin8 }(\sin16) \approx 15052.07464\]

Answer 22

so just round BC to the nearest foot for that answer...

and now that you have BC, you can solve for CD with sin24=CD/BC