College Math

Solution: It is given that ∠VWT = 41 0 . The measurement of ∠VTU = 2* ∠VWT = 2*41 = 82 0 as the angle made by an arc on the circumference of the circle is half of the angle made by same arc on the center of the circle. Now ∠UTW = 180 and ∠UTW = ∠UTV + ∠VTW 180 = 82 + ∠VTW ∠VTW = 180 – 82 = 98 0 8. b Solution: The figure can be split into two parts--that is, the triangle and a semi-circle. The area of the triangle will be calculated using the formula: ½*base*height, where base = 8 and height = 7. Hence, area of triangle = ½*8*7 = 28ft 2 Now, the area of the semi- circle = ½* area of circle. Area of circle = πr 2 where, r = 8/2 = 4 ft Area of semi- circle = ½* 22/7*4 2 Area of semi- circle = 25.14 ft 2 Hence, the area of the given shape = 28 + 25.14 = 53.14 ft 2

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