Answer:
Step-by-step explanation:
We are given that:
And that the two angles <em>A</em> and <em>B</em> are both in QI (positive acute angles).
Given this, we want to determine the value of sin(A + B).
Recall that cosine is the ratio of the adjacent side to the hypotenuse. Using this information, we can determine the opposite side with respect to <em>A:</em>
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Likewise, for <em>B</em>, tangent gives the ratio of the opposite side to the adjacent. Using this information, we can determine the hypotenuse of <em>B:</em>
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In conclusion:
With respect to <em>A</em>, the adjacent side is 60, the opposite side is 11, and the hypotenuse is 61.
With respect to <em>B, </em>the adjacent side is 28, the opposite side is 45, and the hypotenuse is 53.
We can rewrite our original expression as:
And since <em>A</em> and <em>B</em> are both in QI, all trigonometric ratios will be positive.
Using the above conclusions, substitute:
Simplify. Hence: