The laws of cosines and law of sines can be used given that two sides
and an included angle, or two angles a side are known.
Response:
1. The other angles in the triangle formed by the buoy are approximately;
- <u>31.1° and 40.9°</u>
2. Distance of the helicopter from the first island is approximately;
- <u>14.5 miles</u>
Given parameters are;
Distance of the buoy from the easternmost point of a boat = 19 yards
Distance of the buoy from the westernmost point of the other boat = 15 yards
Angle formed from the buoy to the two boats = 108°
Distance between the two boats, <em>d</em>, is given by the law of cosines, as follows;
d² = 19² + 15² - 2 × 19 × 15 × cos(108°) = 586 - 570·cos(108°)
d = √(586 - 570·cos(108°))
By the law of Sines, we have;
Which gives;
The o
The other angles formed in the triangle containing the buoy are;
- θ₁ ≈ <u>31.1</u>
- θ₂ ≈ 180° - 108° - 31.1° ≈<u> 40.9°</u>
2. Distance between the two islands = 20 miles
Angle of elevation with one island = 15°
Angle of elevation with the second island = 35°
Required:
The mileage (distance travelled) of the helicopter.
Solution:
Let <em>A</em> represent the island that has an angle of elevation to the helicopter
of 15°, and let <em>B</em> represent the other island.
Angle formed by the helicopter and the two island, θ, is found as follows;
θ = 180° - (15° + 35°) = 130°
By the Law of Sines, we have;
Which gives;
- The mileage of the helicopter from the first island is approximately <u>14.5 miles</u>
Learn more about the Law of Sines and Cosines here: