To solve the given questions, either of the trigonometric functions; sine, cosine and tangent of an angle has to be applied appropriately to either of the questions. The answers to the questions are:
5. x = 25.60
6. x = 11.00
7. x = [tex]41.8^{o}[/tex]
8. x = [tex]64.2^{o}[/tex]
9. x = [tex]12.8^{o}[/tex]
10. x = [tex]51.3^{o}[/tex]
The questions given are right angled triangles which requires the application of trigonometric functions appropriately. A right angle triangle is one that has one of its angles to be [tex]90^{o}[/tex].
So, each of the questions can be solved as follows:
5. Tan θ = [tex]\frac{opposite}{adjacent}[/tex]
Tan 52 = [tex]\frac{x}{20}[/tex]
⇒ x = Tan 52 * 20
= 25.5988
x = 25.60
6. Sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]
Sin 27 = [tex]\frac{5}{x}[/tex]
⇒ x = [tex]\frac{5}{Sin 27}[/tex]
= 11.0134
x = 11.00
7. Sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]
Sin x = [tex]\frac{4}{6}[/tex]
= 0.66667
x = [tex]Sin^{-1}[/tex] 0.66667
= [tex]41.8^{o}[/tex]
x = [tex]41.8^{o}[/tex]
8. Tan θ = [tex]\frac{opposite}{adjacent}[/tex]
Tan x = [tex]\frac{29}{14}[/tex]
= 2.0714
x = [tex]Tan^{-1}[/tex] 2.0714
= [tex]64.2^{o}[/tex]
x = [tex]64.2^{o}[/tex]
9. Sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]
Sin x = [tex]\frac{12}{54}[/tex]
= 0.22222
x = [tex]Sin^{-1}[/tex] 0.22222
= [tex]12.8^{o}[/tex]
x = [tex]12.8^{o}[/tex]
10. Cos θ = [tex]\frac{adjacent}{hypotenuse}[/tex]
Cos x = [tex]\frac{25}{40}[/tex]
= 0.625
x = [tex]Cos^{-1}[/tex] 0.625
= [tex]51.3^{o}[/tex]
x = [tex]51.3^{o}[/tex]
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