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1 answer:
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<u><em>Answer:</em></u>
Area of shaded region = 220.16 ft²
<u><em>Explanation:</em></u>
The diagram associated with this question is shown in the attached image
Unit in diagram is ft, so I'll use this unit in the answer
We are given that a circle with radius 16 ft is inscribed in a square
We know that the radius of an inscribed circle in a square is equivalent to half the length of the side of the square
<u>This means that:</u>
side length of the square = 2 × radius = 2 × 16 = 32 ft
<u>From the diagram, we can note that:</u>
area of shaded region = area of square - area of circle .............> equation I
<u>1- getting area of square:</u>
Area of a square is the square of its side length
<u>This means that:</u>
Area of square = (32)² = 1024 ft²
<u>2- getting the area of the circle:</u>
Area of circle = πr² = 3.14 × (16)² = 803.84 ft²
<u>3- getting area of shaded region:</u>
<u>Use equation I</u>
area of shaded region = area of square - area of circle
area of shaded region = 1024 - 803.84 = 220.16 ft²
Hope this helps :)
Answer:
<u>8,764.53 feet</u>
Step-by-step explanation:
See the attached figure which represents the question.
Let the distance between campsite and the base of the mountain = d
The total height = 6842 + 5.6 = 6,847.6 feet.
As shown at the graph, the angle x and the depression angle are alternate angles, so they are congruent.
∴∠x = 38°
tan x = opposite/adjacent = (total height)/d = 6847.6/d
So, d = 6847.6/tan x
= 6847.6/tan 38° = 8,764.53 feet (to the nearest hundredth)
so, the distance between campsite and the base of the mountain = 8,764.53 feet
