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21 April, 20:04

Solve the triangle if b=5 and angle B=10°.

A. a=5.0771, c=28.7939

B. a=28.7939, c = 28.3564

C. a=28.3564, c = 5.0771

D. a = 28.3564, c = 28.7939

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Answers (1)
  1. 21 April, 23:14
    0
    Solving the right triangle, the correct answer is option:

    D. a=28.3564, c=28.7939

    Step-by-step explanation:

    Hypotenuse: c

    sin B = (Opposite leg to B) / Hypotenuse

    sin B = b / c

    Replacing the given values:

    sin 10° = 5 / c

    Solving for c: Cross multiplication:

    c sin 10° = 5

    Dividing both sides by sin 10°:

    c sin 10° / sin 10° = 5 / sin 10°

    c = 5 / sin 10°

    c = 5 / 0.173648178

    c = 28.79385236

    Using the Pythagoras Theorem:

    a^2+b^2=c^2

    a^2+5^2=28.79385236^2

    a^2+25=829.0859337

    Solving for a: Subtracting 25 both sides of the equation:

    a^2+25-25=829.0859337-25

    a^2=804.0859337

    Squart root both sides of the equation:

    sqrt (a^2) = sqrt (804.0859337)

    a=28.35640904

    Rounding the values to four decimal places:

    a=28.3564

    c = 28.7939
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