Mathematics
stryker
39

How do I solve this step by step and show my work ?

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(1) Answers
TarahDyke138

Here's my step-by-step approach to this problem: 1) Find ∠EDH (sine) 2) Find ∠EHD (int. ∠s) 3) Find ∠FGH (cosine) 4) Find ∠FHG (int. ∠s) 5) ∠DHG is ∠DHE (EHD) + ∠FHG To find ∠EDH, I have the side opposite and the hypotenuse, so I can use inverse sine to find its angle measure, [latex]sin^{-1}(\frac{32}{49}) = 40.77[/latex] ∠EHD = 180 - 90 - 40.77 = 49.23° To find ∠FGH, I have the adjacent side and the hypotenuse, so I can use inverse cosine. [latex]cos^{-1}(\frac{38}{43}) = 27.91[/latex] ∠FHG = 180 - 90 - 27.91 = 62.09° Now we have two angles we can add to get ∠DHG: ∠DHG = ∠EHD + ∠FHG = 49.23 + 62.09 = 111.32° Did that make sense? Need anything else?

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