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4 July, 19:36

In ΔQRS, r = 510 cm, ∠S=5° and ∠Q=15°. Find the area of ΔQRS, to the nearest centimeter.

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  1. 4 July, 23:28
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    Answer: The area is 8,652 square centimeters (rounded off to the nearest centimeter)

    Step-by-step explanation: The triangle has one side given and two angles given as well. The third angle can be calculated as follows;

    Angle R = 180 - (5 + 15)

    Angle R = 180 - 20

    Angle R = 160

    To calculate side s we shall apply the Sine rule.

    s/SinS = r/SinR

    s/Sin5 = 510/Sin160

    By cross multiplication we now have

    s = (510 x Sin5) / Sin160

    s = (510 x 0.0872) / 0.3420

    s = 44.472/0.3420

    s = 130

    Next we calculate side q as follows;

    q/SinQ = r/SinR

    q/Sin15 = 510/Sin160

    By cross multiplication we now have

    q = (510 x Sin15) / Sin160

    q = (510 x 0.2588) / 0.3420

    q = 131.988/0.3420

    q = 385.929

    q = 386 (approximately)

    Having found all three sides of the triangle as 130, 386 and 510 respectively the area shall be calculated by use of the Heron's formula which is;

    A = [square root] s (s - a) (s - b) (s - c)

    Where s is the semi-perimeter, a, b and c are the three sides. The semi-perimeter is calculated as follows;

    s = (130 + 386 + 510) / 2

    s = 1026/2

    s = 513

    The area now becomes

    A = [square root] 513 (513 - 510) (513 - 386) (513 - 130)

    A = [square root] 513 (3) (127) (383)

    A = [square root] 74858499

    A = 8652.0806

    Rounded to the nearest centimeter, the area of the triangle is 8,652 square centimeters.
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