Question

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?

Answer 1

9514 1404 393

Answer:

• AB = 16.25
• HI = 12.22

Step-by-step explanation:

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

__

1. Cos = Adjacent/Hypotenuse

  cos(52°) = AC/AB

  AB = AC/cos(52°) = 10.01/0.616

  AB = 16.25

__

2. Tan = Opposite/Adjacent

  tan(42°) = GH/HI = 11/HI

  HI = 11/tan(42°) = 11/0.90

  HI ≈ 12.22