1026 Apply inverse trigonometric ratios to find missing
- Slides: 8
10/26: Apply inverse trigonometric ratios to find missing angle measures of right triangles. Do Now Agenda On your desk: HW Quiz & Check - Pencil & Calculator - HW due today -Today’s Notes Get ready for HW Quiz! Homework Handout Guided Notes Independent Practice Exit Ticket! Quiz MONDAY! (start studying NOW)
We will learn to… • Apply inverse trigonometric ratios to find missing angle measures of right triangles.
side lengths We can apply trig ratios to find missing _____ of _____ triangles. right We can apply inverse trig ratios to find missing angle measures right _______ of ______ triangles.
Inverse Trigonometric Ratios: ”inverse” • Inverse Sine: • Inverse Cosine: • Inverse Tangent: Inverse Trig on Calculator: 2 nd sin, cos, or tan
Example 1: Find the measures of A and C. Finding m A: Finding m C: Opposite = 15 Opposite = 20 Adjacent = 15 tan A = tan-1 15 20 = m A tan C = tan-1 36. 87° = m A Check answers using Triangle Angle Sum Theorem: 36. 87° + 53. 13° + 90° = 180° ✔ 20 15 = m C 53. 13° = m C
Example 2: Find the measures of D and F. Finding m D: Finding m F: Adjacent = 10 Opposite = 10 Hypotenuse = 17 10 cos D = cos-1 10 17 sin F = 17 = m D sin-1 53. 97° = m D Check answers using Triangle Angle Sum Theorem: 53. 97° + 36. 03° + 90° = 180° ✔ 10 17 = m F 36. 03° = m F
We can apply inverse trig ratios to find missing _______ of ______ triangles. right angle measures Steps for Success: 1. Verify that the triangle is right. 3. Label sides (hypotenuse, opposite, adjacent) 4. Write equation w/trig ratio 5. Apply inverse trig ratio (2 nd button in calc) 6. Round answer 7. Check using the triangle sum theorem.
