which mountains peaks can be seen from Oahu.
Island Distance(Mi) Mountain Height(ft)
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.
Could someone go through the steps to solve this?
I have already done so but I seem to get close but different answers I need to check my work.
Assume that the observer is at sea-level.
The horizontal line is tangent to the earth at Oahu,
distance = 40 miles = 40*5280'=211200'
The radius of the earth is
r=3960 miles=20908800'
and is perpendicular to the horizontal line above.
Hypotenuse
=sqrt(211200²+20908800²)
=2745600√(58)'
Visible height
= hypotenuse - radius of earth
= 1066.64' < 4961
Therefore the said peak is visible.
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 draw me a diagram and explain to me what to do step by step? please and thank you!!
To determine which mountain peaks can be seen from Oahu, we need to use some trigonometry and the given information:
1) Determining the angle formed at the center of the earth:
The distance between Oahu and Molokai is given as 40 miles. We can consider this distance as the length of the adjacent side of a right triangle, where the central angle at the center of the earth forms the other side. The hypotenuse of this right triangle is the radius of the earth.
Using the formula for tangent (tan(theta) = opposite/adjacent), we can solve for theta:
tan(theta) = opposite / adjacent
tan(theta) = radius of the earth / distance between Oahu and Molokai (40 miles)
tan(theta) = 3960 mi / 40 mi
To find theta, we need to inverse the tangent function (tan^(-1)), also known as the arctan function:
theta = arctan(3960/40)
Using a calculator or an online arctan calculator, we find that theta is approximately 88.4 degrees.
So the angle formed at the center of the earth is approximately 88.4 degrees.
2) Determining the length of the hypotenuse:
The hypotenuse of the right triangle is the radius of the earth, which is given as 3960 miles. This is the length we need to find.
We can use the cosine function to solve for the hypotenuse:
cos(theta) = adjacent / hypotenuse
cos(88.4 degrees) = 40 mi / hypotenuse
To solve for the hypotenuse, we isolate it:
hypotenuse = 40 mi / cos(88.4 degrees)
Using a calculator or an online cosine calculator, we find that cos(88.4 degrees) is approximately 0.0342.
Therefore, the length of the hypotenuse (radius of the earth) is:
hypotenuse = 40 mi / 0.0342
Simplify this expression to find the length of the hypotenuse.
By plugging the values we obtained into the formulas, you should be able to confirm if your calculations were correct.