Answer:
θ ≈ 31.1°
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relations between triangle sides and trig functions of angles. Here, you have the side opposite the angle, and you have the hypotenuse. So, the relevant relation is ...
Sin = Opposite/Hypotenuse
sin(θ) = 2/√15
The inverse sine function is used to find the angle value from it sine:
θ = arcsin(2/√15) ≈ 31.0909°
The angle θ is about 31.1°.
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Comment on inverse trig functions
When you use your calculator for inverse trig functions, be sure it presents angles in the units you want. You may have to go to some effort to ensure that the angle is expressed in degrees (not radians).
