You fly a hot air balloon 0.5 miles above the ground. What is the measure of BD⌢, the portion of Earth that you can see? Round y
our answer to the nearest tenth. (Earth's radius is approximately 4000 miles.)
PLEASE HELP ASAP!
PLEASE HELP ASAP!
1 answer:
Step-by-step explanation:
To solve this problem, we need the angle CAD, which can then be used to calculate the arc BD.
From definition of cosine,
cos(x) = adjacent / hypotenuse
cos(x) = AD / AC = 4000 / 4000.5 = 0.9998750156230471
The inverse function gives
x = arccosine (4000/4000.5)
= arccosine (0.9998750156230471)
= 0.01581056485742214 radians = 0.9058786380481468 degrees
Radius of the earth, r = 4000 miles
Arc BD = 2 time arc subtended by angle x
= 2 (rx) where x is in radians
= 2*4000*0.01581056485742214
= 126.48 miles (to two decimal places)
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Answer:
15.43 ft
Step-by-step explanation:
To solve this question, one should use the concept of similar triangles.
The pole's shadow and the distance to the ground (x) form a similar triangle to the distance of the plumb bob from the base and the length of the plumb bob, respectively. Note that we do not need to know the measurements of the third side of the triangles to solve the problem. Therefore, the distance of the top of the pole to the ground is:
The distance of the top of the pole to the ground is 15.43 ft.