So the question is basically asking which mountains peaks can be seen from Oahu.
Island Distance(Mi) Mountain Height(ft)
Lanai - 65 - Lanaihale - 3,370
Maui - 110 - Haleakala - 10,023
Hawaii - 190 - Mauna Kea - 13,796
Molokai - 40 - Kamakou - 4,961
A) Radius of earth= 3960 mi.
Determine angle formed at the center of the earth.
B) Determine length of the hypotenuse.
Is Lanai-hale visible from Oahu?
C) Repeat parts A & B for the other 3 islands
D) Which 3 Mountains are visible from Oahu?
To determine which mountain peaks can be seen from Oahu, we need to analyze the distances and heights of various mountains from Oahu. Let's go step by step to answer the question:
A) Radius of Earth = 3960 mi.
To determine the angle formed at the center of the Earth, we can use trigonometry. The formula to calculate the angle is:
angle = arc distance / radius
For example, for Lanai:
arc distance = 65 mi
radius = 3960 mi
angle = 65 mi / 3960 mi ≈ 0.0164 radians (approximately)
B) Determine the length of the hypotenuse.
The question asks if Lanaihale is visible from Oahu. To determine this, we need to calculate the hypotenuse length using the distance and height of the mountain:
distance = 65 mi
height = 3370 ft
To calculate the length of the hypotenuse, we need to convert the height to miles, as the distance is given in miles:
height in miles = 3370 ft / 5280 ft/mi ≈ 0.6383 mi
Using the distance and height, we can define a right-angled triangle. By using the Pythagorean theorem, we can calculate the length of the hypotenuse:
hypotenuse = sqrt(distance^2 + height^2)
hypotenuse = sqrt((65 mi)^2 + (0.6383 mi)^2)
C) Repeat parts A & B for the other 3 islands.
To determine which other mountains are visible from Oahu, repeat the calculations for the other three islands (Maui, Hawaii, and Molokai).
For each island, calculate:
A) The angle formed at the center of the Earth using the arc distance and radius.
B) The length of the hypotenuse using the distance and height of the mountain.
D) Which 3 mountains are visible from Oahu?
To determine which mountains are visible from Oahu, we need to compare the calculated angles and lengths of the hypotenuse for each island's mountain.
If the angle formed and the length of the hypotenuse are within the visual range from Oahu, then the respective mountain peak is visible.
By comparing the calculated values obtained in steps A and B for each mountain peak, you can determine which three mountains (out of Lanaihale, Haleakala, Mauna Kea, and Kamakou) are visible from Oahu.