two boats leave the harbor at 9:00 am. Boat A sails north at 20 km/hr. Boat B sails west at 15km/hr. 158, How far apart are the two boats at noon?
two boats leave the harbor at 9:00 am. Boat A sails north at 20 km/hr. Boat B sails west at 15km/hr. 158, How far apart are the two boats at noon? helpppp
is it 105km?
Not quite. Did you get a distance of 60 km traveled by boat A and 45 km traveled by boat b? And did you then apply the Pathagorean formula (a 2 + b 2 = c 2 )?
I get the distance right for both and then I added them that's how I got 105, but if I do the Pythagorean formula I get 75 km apart, is this the right answer?
Yes! Very good!
2 Answers By Expert Tutors
Kate K. answered • 02/26/13
Let's Work Together: You Can Succeed With the Right Tools and Tutor
North bound : 20km x 3 hours = 60 KM. west bound 15km x 3 hours = 45 km. Now 60^2 + 45^2 = 3,600+ 2025 = 5625. Square root of 5,625 =75. they are 75 km apart. (using the Pythagorean theorem)
John R. answered • 02/16/13
Physics and Math Tutor – Kind, Easy-going, Patient
Be sure to apply the Pythagorean formula: the length of the hippopotamus (hypotenuse) squared is equal to the sum of the squares of the lengths of the legs.
c= √(a 2 + b 2 )
That's what I did thank you!
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<strong>Trigonometry</strong> – Bearings<br />
N<br />
Michael<br />
1. Amanda and Michael leave the same campsite<br />
and set off in different directions.<br />
Michael walks 7 kilometres on a bearing of 035 0<br />
and Amanda walks 8 kilometres due east.<br />
How far apart are Amanda and Michael?<br />
0<br />
35<br />
7 km<br />
8 km<br />
Amanda<br />
2. Two yachts leave harbour H.<br />
Yacht A sails on a bearing of 072 0 for<br />
30 km and then stops.<br />
Yacht B sails on a bearing of 140 0 for<br />
50 km and then stops<br />
30 km<br />
A<br />
How far apart are the two yachts when they<br />
both have stopped?<br />
H<br />
50 km<br />
B<br />
3. Debbie is taking part in an orienteering walk. She leaves checkpoint A and walks<br />
6.8 km due south to checkpoint B.<br />
From B she walks 4.7 km on a bearing of 080 0 .<br />
How far is Debbie from checkpoint A?<br />
4. Mark and Rabnawaz leave a hostel at the<br />
same time.<br />
Mark walks on a bearing of 045 0 at a speed<br />
of 4.4 kmph.<br />
Rabnawaz walks on a bearing of 100 0 at a<br />
speed of 4.8 kmph.<br />
Mark<br />
If both walk at steady speeds, how far apart will they be after 2 hours?<br />
5. The sketch below shows the journey of a ship from a harbour.<br />
100<br />
Harbour<br />
40<br />
The ship leaves the harbour and sails 30 km on a bearing of 040 0 and then sails 50 km<br />
on a bearing of 100 0 .<br />
Calculate the distance the ship is from the harbour.<br />
6. Two ships leave Liverpool at the same time.<br />
One of them travels north-west at an average speed of 10.5 kmph while the other<br />
travels at an average speed of 14 kmph on a bearing of 280 0 .<br />
How far apart are these ships after 3 hours?<br />
7. Three oil platforms, Alpha, Beta and Gamma<br />
are situated in the North Sea.<br />
Beta is 12 km from Alpha and is on a bearing of<br />
145 0 from Alpha.<br />
Gamma is 16 km from Alpha and is on a bearing<br />
of 220 0 from Alpha.<br />
16 km<br />
Gamma<br />
Alpha<br />
12 km<br />
Beta<br />
Find the distance of Beta from Gamma.
8. A submarine is positioned at A.<br />
Its radar detects another ship 50 km away on a<br />
bearing of 145 0 , at C.<br />
The submarine informs its base at B, 40 km away<br />
on a bearing of 210 0 , of this ship.<br />
The base informs the submarine to intercept this ship.<br />
How far is the ship at C from the base B?<br />
40 km<br />
210<br />
C<br />
9. David takes part in a cross-country race.<br />
He leaves the starting point of the race<br />
and runs due west for 5.5 km before<br />
changing direction and running 6.3 km<br />
in a north-west direction.<br />
David<br />
6.3 km<br />
Calculate how far David is from the starting point.<br />
5.5 km<br />
Start<br />
10. The diagram shows the position of 3 airports,<br />
A, E and G.<br />
G is 200km from A.<br />
E is 160 km from A<br />
From G the bearing of A is 052 0 .<br />
From A the bearing of E is 216 0 .<br />
200 km<br />
160 km<br />
How far apart are airports G and E?<br />
G<br />
E<br />
11. The diagram shows the position of 3 towns<br />
E, B and F.<br />
300 km<br />
B is 300 km from E and is on a bearing of 046 0<br />
from E.<br />
From E, the bearing of F is 116 0 .<br />
F is due south of B.<br />
Calculate the distance from E to F.<br />
12. A submarine leaves Faslane in Scotland<br />
and sails into the Atlantic Ocean on a bearing<br />
of 250 0 for a distance of 120 km before<br />
changing course and sailing on a bearing of<br />
190 0 for 90 km.<br />
Calculate the distance the submarine is from Faslane.<br />
90 km<br />
190<br />
Faslane<br />
120 km<br />
250<br />
13. An aeroplane flying to Edinburgh is 100 km<br />
due south of Edinburgh when the pilot is told<br />
to change direction because of fog.<br />
He is told to fly to Prestwick on a bearing of 320 0 .<br />
The bearing of Prestwick from Edinburgh is 240 0 .<br />
Prestwick<br />
Edinburgh<br />
100 km<br />
(a) Find the distance of the aeroplane from Prestwick.<br />
(b) Find the bearing of Edinburgh from Prestwick.<br />
Aeroplane<br />
14. A church is 600 metres due west of a flagpole.<br />
A statue is on a bearing of 160 0 from the church<br />
and on a bearing of 220 0 from the flagpole.<br />
600 m<br />
Find the distance of the church from the statue.
15. Three radio masts, K, W and P are situated in the W<br />
Australian outback.<br />
K is 250km due south of W. W is 410km from P.<br />
P is on a bearing of 130° from K.<br />
250 km<br />
Calculate the bearing of P from W.<br />
K<br />
130<br />
410 km<br />
P<br />
16. A ship sails from harbour H on a bearing of<br />
084° for 340km until it reaches point P.<br />
It then sails on a bearing of 210° for 160km<br />
until it reaches point Q.<br />
Calculate the distance between the point Q<br />
and the harbour.<br />
84<br />
340 km<br />
Q<br />
17. Two ships A and B are anchored at sea. B is 65km due east of A. A<br />
lighthouse is positioned on a bearing of 055° from A and on a bearing of 310°<br />
from B.<br />
Calculate how far the lighthouse is from ship B.
18. A ship, at position P, observes a lighthouse at<br />
position Q on a bearing of 040°. The ship travels<br />
30km on a bearing of 125° to position R.<br />
From position R, the ship observes the lighthouse<br />
on a bearing of 340°.<br />
(a) Find the bearing of R from the lighthouse.<br />
(b) Calculate the distance from R to the lighthouse<br />
R<br />
19. A boat sails on a bearing of 160° for 600km before changing course and<br />
sailing 700km on a bearing of 050°.<br />
(a) How far the boat is from its starting point?<br />
(b) Find the bearing the ship is from its starting point.<br />
20. A surveyor is walking due west when he comes<br />
to a marsh. To avoid the marsh he turns at P<br />
and walks for 60m on a bearing of 215°<br />
and then for 85m on a bearing of 290°.<br />
215<br />
85 m<br />
60 m<br />
Calculate PR the direct distance across the marsh.<br />
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<strong>Trigonometry</strong> – Bearings N Michael 1. Amanda and Michael leave the same campsite and set off in different directions. Michael walks 7 kilometres on a bearing of 035 0 and Amanda walks 8 kilometres due east. How far apart are Amanda and Michael? 0 35 7 km 8 km Amanda 2. Two yachts leave harbour H. Yacht A sails on a bearing of 072 0 for 30 km and then stops. Yacht B sails on a bearing of 140 0 for 50 km and then stops N 30 km A How far apart are the two yachts when they both have stopped? H 50 km B 3. Debbie is taking part in an orienteering walk. She leaves checkpoint A and walks 6.8 km due south to checkpoint B. From B she walks 4.7 km on a bearing of 080 0 . How far is Debbie from checkpoint A? 4. Mark and Rabnawaz leave a hostel at the same time. Mark walks on a bearing of 045 0 at a speed of 4.4 kmph. Rabnawaz walks on a bearing of 100 0 at a speed of 4.8 kmph. N Mark If both walk at steady speeds, how far apart will they be after 2 hours? Rabnawaz
- Page 2 and 3: 5. The sketch below shows the journ
- Page 4 and 5: N 12. A submarine leaves Faslane in
- Page 6: 18. A ship, at position P, observes
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SOLUTION: Two boats traveling in the same direction leave a harbor at noon. After 3 hours they are 60 miles apart. If one boat travels twice as fast as the other,find the avarage rate of eac
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