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?
Can someone please draw a diagram and explain to me where the angle formed at the center of the earth and hypotenuse please? I'm really despearate to understand this problem! It's due on Monday! please help! xoxoxo <3
If you draw a line from a point above the surface, to the horizon, the angle where the radius meets the point on the horizon is a right angle, because the line is tangent to the surface of the earth.
So, if you have a point x km above the surface, and the radius of the earth is r km, and the distance from the point to the horizon is d km,
r^2 + d^2 = (r+x)^2
If you need to work with the angle θ at the center of the earth,
sinθ = d/(r+x)
tanθ = d/r
if the first three terms in the expansion of (1+ax)^n in ascending powers
of x are 1+12x+64x^2 find n and a
To understand this problem, let's break it down step by step:
A) To determine the angle formed at the center of the earth, we need to use trigonometry. The formula to find an angle in a right triangle is given as:
sin(angle) = opposite/hypotenuse
In this case, the opposite side is the distance between Oahu and the other islands, and the hypotenuse is the radius of the earth. So, we can use the formula:
sin(angle) = distance/hypotenuse
To find the angle, we can solve for it by taking the inverse sine (or arcsine) of the ratio:
angle = arcsin(distance/hypotenuse)
Using the given distances and the radius of the earth (3960 mi), you can calculate the angles formed at the center of the earth for each island mentioned.
B) To determine the length of the hypotenuse, we need to use the Pythagorean theorem. In a right triangle, the sum of the squares of the two legs (sides adjacent to the right angle) is equal to the square of the hypotenuse.
The Pythagorean theorem can be written as:
hypotenuse^2 = leg1^2 + leg2^2
In this case, the legs are the distances between Oahu and the other islands. By plugging in the values for the distances, you can solve for the length of the hypotenuse.
C) Repeat parts A and B for the other three islands, Maui, Hawaii, and Molokai, using the corresponding distances provided.
D) To determine which mountains are visible from Oahu, you need to compare the angles calculated in part A with the angles that correspond to the heights of the mountains. If the angle calculated is larger than or equal to the angle formed by the mountain, it means that the mountain will be visible from Oahu.
For example, if the angle calculated for Lanai is greater than or equal to the angle formed by the Lanaihale mountain, then the Lanaihale mountain is visible from Oahu. Repeat this comparison for each mountain and island to identify which mountains are visible.