Answer: the height of the lighthouse is 838.8 feet
Step-by-step explanation:
The right angle triangle ABC illustrating the scenario is shown in the attached photo.
The angle of depression and angle A are alternate angles, hence, they are the equal.
The height, h of the lighthouse represents the opposite side of the right angle triangle. The distance of the boat from the foot of the lighthouse represents the adjacent side of the right angle triangle.
To determine h, we would apply
the tangent trigonometric ratio.
Tan θ, = opposite side/adjacent side. Therefore,
Tan 62 = h/446
h = 446tan62 = 446 × 1.8807
h = 838.8 feet to the nearest tenth.
Answer:
- arc second of longitude: 75.322 ft
- arc second of latitude: 101.355 ft
Explanation:
The circumference of the earth at the given radius is ...
2π(20,906,000 ft) ≈ 131,356,272 ft
If that circumference represents 360°, as it does for latitude, then we can find the length of an arc-second by dividing by the number of arc-seconds in 360°. That number is ...
(360°/circle)×(60 min/°)×(60 sec/min) = 1,296,000 sec/circle
Then one arc-second is
(131,356,272 ft/circle)/(1,296,000 sec/circle) = 101.355 ft/arc-second
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Each degree of latitude has the same spacing as every other degree of latitude everywhere. So, this distance is the length of one arc-second of latitude: 101.355 ft.
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<em>Comment on these distance measures</em>
We consider the Earth to have a spherical shape for this problem. It is worth noting that the measure of one degree of latitude is almost exactly 1 nautical mile--an easy relationship to remember.
Answer:
- 35
- x 100
- 00
- 500
Step-by-step explanation:
35 divided by 7 is 5. 3,500 is 35 x 100. 35 hundreds (3,500) divided by 7 is 5 hundred (5 with 00 at the end). 3,500 divided by 7 is 500.
Hope it helps!
The original value of the sum is $131.1273...
Rounded up that is $131.13
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