A passenger on a cruise ship is positioned 42m above sea level and is admiring a tropical island in the distance.
One end of the island is at a bearing of 028° and has an angle of depression of 11°, while the other is at a true
bearing of 118° and has an angle of depression of 19°. How long is the island?
I can't draw it out!! thx for ur help guys!!
distance to one end ... 42 m / tan(11º)
distance to other end ... 42 m / tan(19º)
118º - 28º = 90º ... the length of the island is the hypotenuse
(length)^2 = (one distance)^2 + (other distance)^2
d1 + d2. = Hor. distance from cruise to far end of island.
d2 = length of island.
Tan19 = 42/d1,
d1 = 122 m.
Tan11= 42/(d1+d2).
d1+d2 = 216 m.
d2 = 216-d1 = 216-122 = 94 m = Length of island.
To find the length of the island, we can use trigonometry and the concept of angles of depression.
Let's break down the problem step by step:
1. Draw a diagram: Sketch a diagram of the situation described. Draw a line representing the sea level and label the height of the passenger (42m) above it. Mark two points on the sea level, representing the ends of the island.
2. Calculate the distances from the passenger to each end of the island: Use trigonometry to calculate the distances from the passenger to each end of the island.
- For the end of the island with a bearing of 028° and an angle of depression of 11°, we have a right-angled triangle. The height of the passenger (42m) is the side opposite the angle of depression, while the distance from the passenger to the end of the island is the hypotenuse. We can use the tangent function to find this distance:
Tangent(angle) = Opposite side / Adjacent side
In this case, tan(11°) = 42m / x
Solving for x, we can find the distance from the passenger to this end of the island.
- Apply the same logic to the end of the island with a bearing of 118° and an angle of depression of 19°. Use the tangent function to find the distance from the passenger to this end of the island.
3. Add the distances to get the length of the island: Once you have found the distances from the passenger to each end of the island, add them together to get the total length of the island.
In summary, to find the length of the island, use trigonometry to calculate the distances from the passenger to each end of the island and then add those distances together.