University:
High School
Course:
High School Geometry
Academic year:

2020
Views:

69

Pages:

2
Author:

vigtelkeiyr

Inverse Pre - Solving Right Triangles In your own words, write the meaning of each vocabulary term. Inverse: the opposite Operations: Addition (+): - Subtraction (-): + Multiplication (x): ÷ Division (÷): x Square (x²): √ Core Concepts Inverse Trigonometric Ratios to find the missing angles Let ∠A be an acute angle. Inverse Tangent: If tan A = x, then tan⁻¹x = ∠A tan⁻¹(tan A) = tan⁻¹(x) tan⁻¹(BC/AC) = m∠A Inverse Sine: If sin A = y, then sin⁻¹y = ∠A sin⁻¹(BC/AB) = m∠A Inverse Cosine: If cos A = z, then cos⁻¹z = ∠A cos⁻¹(AC/AB) = m∠A 8.6 Practice - Inverse Trig 1. The cosine of one of the two acute angles is 1/5. Determine which of the two acute angles has the given trigonometric ratio. Diagram of a right triangle labeled with vertices E, F, and G cos F = adj/hyp Cos F will work 2. The sine of the angle is about 0.38. Diagram of a right triangle with sides labeled 2√3, √2, and √14 sin = opp/hyp sin F = 2√3/√14 ≈ 3.46/3.74 ≈ .92 sin E = √2/√14 ≈ 1.41/3.74 ≈ .38 In Exercises 3-6, let ∠H be an acute angle. Use a calculator to approximate the measure of ∠H. 3. sin H = 0.2 sin⁻¹(sin H) = sin⁻¹(0.2) ∠H = sin⁻¹(0.2) ∠H ≈ 11.54° 4. tan H = 1 tan⁻¹(tan H) = tan⁻¹(1) ∠H = tan⁻¹(1) ∠H = 45° 5. cos H = 0.33 cos⁻¹(cos H) = cos⁻¹(0.33) ∠H = cos⁻¹(0.33) ∠H ≈ 70.73° 6. sin H = 0.89 sin⁻¹(sin H) = sin⁻¹(0.89) ∠H = sin⁻¹(0.89) ∠H ≈ 62.87° 11. A boat is pulled in by a winch on a dock 12 feet above the deck of the boat. When the winch is fully extended to 25 feet, what is the angle of elevation from the boat to the winch? Diagram of a right triangle with sides labeled 12 and 25 sin = opp/hyp sin x = 12/25 sin⁻¹(sin x) = sin⁻¹(12/25) x = sin⁻¹(12/25) x ≈ 28.69°