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In right triangle ABC, ∠C is a right angle, m∠A=52∘, AC=10.01, and AB=c.
sin52∘≈0.788
cos52∘≈0.616
tan52∘≈1.280
What is the measurement of AB?


In right triangle GHI, ∠H is a right angle, m∠I=42∘, and GH=11.
sin42∘≈0.67
cos42∘≈0.74
tan42∘≈0.90
What is the measurement of HI?

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sqdancefan

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Answer:

  • AB = 16.25
  • HI = 12.22

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relevant relationships.

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1. Cos = Adjacent/Hypotenuse

  cos(52°) = AC/AB

  AB = AC/cos(52°) = 10.01/0.616

  AB = 16.25

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2. Tan = Opposite/Adjacent

  tan(42°) = GH/HI = 11/HI

  HI = 11/tan(42°) = 11/0.90

  HI ≈ 12.22

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