Question

You conclude a triangle is 7 cm long and 3.5 tall. Use these measurements to estimate the six trigonometric ratios of θ. (Round your answers to two decimal places.)

Answer 1

• sin(θ) = 0.45
• cos(θ) = 0.89
• tan(θ) = 0.50
• csc(θ) = 2.24
• sec(θ) = 1.12
• cot(θ) = 2.00

Explanation:

The Pythagorean theorem tells you the length of the hypotenuse of the triangle:

AC² = AB² + BC²

AC² = (7 cm)² +(3.5 cm)²

AC = √(61.25 cm²) = 3.5√5 cm ≈ 7.8262 cm

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The mnemonic SOH CAH TOA reminds you of the definitions of three of the trig functions. The remaining functions are their reciprocals.

• sin(θ) = BC/AC ≈ 3.5/7.8262 ≈ 0.45 (Opposite/Hypotenuse)
• cos(θ) = AB/AC ≈ 7/7.8262 ≈ 0.89 (Adjacent/Hypotenuse)
• tan(θ) = BC/AB = 3.5/7 = 0.50 (Opposite/Adjacent)
• csc(θ) = 1/sin(θ) ≈ 2.24
• sec(θ) = 1/cos(θ) ≈ 1.12
• cot(θ) = 1/tan(θ) = 2.00