SOLUTION: Find the measure of obtuse angle θ, given that sinθcos30° + cosθsin30° = √2/2

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Question 1194582: Find the measure of obtuse angle θ, given that sinθcos30° + cosθsin30° = √2/2
Answer by ikleyn(52908) About Me  (Show Source):
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Find the measure of obtuse angle θ, given that sinθcos30° + cosθsin30° = √2/2
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You are given that 

    sin(θ)*cos(30°) + cos(θ)*sin(30°) = √2/2.


Using the formula for the sum of arguments for sine function, it is the same as

    sin(θ + 30°) = sin(45°)

or

    sin(θ + 30°) = sin(135°).


It implies that 

    θ + 30° = 45°  or  θ + 30° = 135°.


Since  θ  is an obtuse angle  (which means  90° < θ < 180°),  it implies that  θ = 135° - 30° = 105°.    ANSWER

Solved and explained.