Answer:
(a) sin(32°) = 8.5/x
Step-by-step explanation:
In the right triangle, the angle (32°), side opposite (8.5), and hypotenuse (x) are given. The trig relation that relates these is ...
Sin = Opposite/Hypotenuse
sin(32°) = 8.5/x
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Additional comment
The mnemonic SOH CAH TOA was invented to remind you of the trig relations:
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent
For a problem like this, identify the marked sides and angle and their relation to each other. Then you can choose the appropriate trig relation.
If you're asked to find the angle, the inverse relation is used.
sin(x) = 8.5/16
x = arcsin(8.5/16) ≈ 32° . . . . . arcsin is the inverse sine function
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Please note that sin(32) is very different from sin(32°). An argument of a trig function that has no units (a pure number) should be considered to be an angle in radians. 32 radians is about 1833.4649°. This will have the same trig function values as 33.4649°, so would give you wrong answers. In short, none of the offered equations is true relative to the figure. The true equation is ...
[tex]\sin(32^\circ)=\frac{8.5}{x}[/tex]
