(image) The figure below is an isosceles triangle surmounted by a semi-circle. Find the area of the entire region.
1 answer:
Answer:
12.53
Step-by-step explanation:
∠BCA = (180°-40°)/2 = 70°
Laws of Sines: CA/sin 40° = AB/sin 70° = 5/sin 70°
CA = 5/sin 70° * sin 40° = 3.40
area of semicircle CA = (3.1416 * 1.70²) / 2 = 4.54
By Heron's Formula, area of triangle ABC:
1/4 √(a+b+c) (a+b-c) (b+c-a) (c+a-b) = 1/4 * √13.4*3.4*3.4*6.6
= 7.99
Entire region area = 4.54 + 7.99 = 12.53
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<u><em>Answer:</em></u>
The bird is approximately 9 ft high up in the tree
<u><em>Explanation:</em></u>
The required diagram is shown in the attached image
Note that the tree, the cat and the ground form a right-angled triangle
<u>Therefore, we can apply special trigonometric functions</u>
<u>These functions are as follows:</u>
<u>Now, taking a look at our diagram, we can note the following:</u>
α = 25°
The opposite side is the required height (x)
The adjacent side is the distance between the cat and the tree = 20 ft
Therefore, we can use the <u>tan function</u>
<u>This is done as follows:</u>
which is 9 ft approximated to the nearest ft
Hope this helps :)
