Answer:
A
Step-by-step explanation:
Using the tangent and sine ratios in the right triangle and
tan30° = [tex]\frac{1}{\sqrt{3} }[/tex], sin30° = [tex]\frac{1}{2}[/tex]
tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{5}{b}[/tex]
Multiply both sides by b
b × tan30° = 5, that is
b × [tex]\frac{1}{\sqrt{3} }[/tex] = 5
Multiply both sides by [tex]\sqrt{3}[/tex]
b = 5[tex]\sqrt{3}[/tex]
and
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{5}{c}[/tex]
Multiply both sides by c
c × sin30° = 5, that is
c × [tex]\frac{1}{2}[/tex] = 5 ( multiply both sides by 2 )
c = 10
Option (1) will be the correct option.
Find the sine of the angle measuring 30°,
[tex]\text{sin}(30^\circ)=\frac{\text{Opposite side}}{\text{Hypotenuse}}=\frac{5}{c}[/tex]
[tex]\frac{1}{2}=\frac{5}{c}[/tex]
[tex]c=10[/tex]
Similarly, find cosine of the given angle,
cos(30°) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}=\frac{b}{c}[/tex]
[tex]\frac{\sqrt{3} }{2}=\frac{b}{10}[/tex]
[tex]b=\frac{10\sqrt{3} }{2}[/tex]
[tex]b=5\sqrt{3}[/tex]
Therefore, Option (1) will be the correct option.
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