# trigonometry

posted by .

2. two look out situations, which are 25 miles apart along the coast on a north-south shoreline, spot an approaching yacht. One lookout station measures the direction to the yacht at N33 degrees E, and the other station measures the direction of the yacht at S62 degrees E. How far is the yacht from each lookout station? how far is the yacht from the coast?

• trigonometry -

make a sketch, label the side across from the 33º angle as x, and the side across the 62º as y.
Using the sine law
x/sin33 = 25/sin85

do y the same way.

draw a perpendicular from the boat to shore, giving you a right-angled triangle, call it h

sin 62 = h/x
h = xsin62, and since we know x ....

## Similar Questions

a yacht is sailing at a speed of 12 knots due south in calm water. if the tacht encounters a current of 4 knots from bearing 040 degrees: determine the resultant speed and direction of the yacht. here is my answers: 15.28 knots from …
2. ### math

a fire is sighted from two ranger stations that are 6000 meters apart. The angles of observation to the fire measure 52 degrees from one station and 41 degrees from the other station. Find the distance along the line of sight to the …
3. ### math

two look out situations, which are 25 miles apart along the coast on a north-south shoreline, spot an approaching yacht. One lookout station measures the direction to the yacht at N33 degrees E, and the other station measures the direction …
4. ### Math Trig

A coast guard patrol boat is 14.8 km east of the Brier Island Lighthouse. A disabled yacht is 7.5km south of the lighthouse. a) How far is the patrol boat from the yacht, to the nearest tenth of a kilometer?
5. ### math

Two lookout stations, which are 25 miles apart along the coast on a north-south line, spot an approaching yacht. One lookout station measures the direction to the yacht at N 33degrees E, and the other station measures the direction …
6. ### Math

A lighthouse is east of a Coast Guard patrol boat. The Coast Guard station is 20 km north of the lighthouse. The radar officer aboard the boat measures the angle between the lighthouse and the station to be 23°. How far is the boat …
7. ### Trigonometry

Two radar stations are 50 miles apart. Both are tracking the same plane. At this moment, the angle between station 1 and the plane is 73 degrees and the angle between station 2 and the plane is 46 degrees. How far is the plane from …
8. ### Math

A yacht is moving at 10kmh in a south easterly direction and encounters a 3kmh current from the north. Find the actual speed and direction of the yacht.
9. ### maths

a yacht is moving at 10km/h in a south easterly direction and encounters a 3km/h current from the north. find the actual speed and direction of the yacht
10. ### Trig application

I am having trouble with this question. A privately owned yacht leaves a dock in Myrtke Beach, South Carolina, and heads toward Freeport in the Bahamas at a bearing of S 1.4 degrees E. The yacht averages a speed of 20 knots over the …

More Similar Questions