The summit of Mount Mauna Kea is approximately 13,796 ft above sea level. What is the distance from the summit to the horizon, rounded to the nearest mile? Assume that the distance from Earth's center to any point on Earth's surface is 4,000 miles.

distance from the summit to the horizon = 145 miles

Step-by-step explanation:

I have attached a diagram to depict the question;

We are given that the distance from Earth's center to any point on Earth's surface is 4,000 .

Thus, the value of r in the diagram is; r = 4000 miles

Now we are also told that the summit of Mount Mauna Kea is approximately 13,796 ft above sea level. Thus, v in the diagram is v = 13,796 ft.

Since r is in miles, let's convert it to miles too.

Thus, v = 13796 x (1/5280) = 2.612879 miles

Thus, v + r = 2.612879 miles + 4000 miles = 4002.612879 miles

we are trying to find the distance from the summit to the horizon. In the diagram, it is represented by the side OH.

Thus, using Pythagoras theorem, we have;

(OH)² + r² = (v + r)²

Thus,plugging in the values and rearranging;

(OH)² = 4002.612879² - 4000²

(OH)² = √20909.85913666699

OH = 144.6 miles ≈ 145 miles

answer: i'm not going to give you the answer, but some hints to work it out.

step-by-step explanation: so, if there is a straight line that means that the line angle is 180°. so we subtract the 2 angle measures provided, (15 and 38) from 180. so the answer is 180 - (38 + 15). (you have to solve the equation)

welll its a very hard question but ill

step-by-step explanation:

first you take the 6 dollars and add 10 to it then add the 50 to that then multiply by 8 with xy and your answer will be

hope this