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Lesson 9.1 Use Trigonometry with Right Triangles

Lesson 9.1 Use Trigonometry with Right Triangles. Standard Accessed: Students will prove, apply, and model trigonometric functions and ratios. Warm-Up. Lesson Presentation. Lesson Quiz. Warm-Up.

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Lesson 9.1 Use Trigonometry with Right Triangles

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  1. Lesson 9.1Use Trigonometry with Right Triangles Standard Accessed: Students will prove, apply, and model trigonometric functions and ratios. Warm-Up Lesson Presentation Lesson Quiz

  2. Warm-Up In right triangle ABC, a and b are the lengths of the legs and c is the length of the hypotenuse. Find the missing length. Give exact values. 1. 2. 3.If you walk 2.0 kilometers due east and then 1.5 kilometers due north, how far will you be from your starting point. 1. distance formula

  3. Vocabulary

  4. Essential Understandings How are trigonometric functions used in right triangles? • The six trigonometric ratios: sine, cosine, tangent, cosecant, secant, and cotangent, are the six possible ratios of pairs of sides of a right triangle. • If you know the length of any side and the measure of either of the acute angles, you can find all the remaining parts of a right triangle.

  5. 1 EXAMPLE Evaluate trigonometric functions Evaluate the six trigonometric functions of the angle . 25 SOLUTION 3. 1. 2. 6. 4. 5.

  6. 2 EXAMPLE Evaluate trigonometric functions If is an acute angle of a right triangle and , what is the value of ? SOLUTION a. b. c. d.

  7. Geometry Conjectures Isosceles Right Triangle: In an isosceles right triangle, if the legs have length , then the hypotenuse has length . : In a triangle, if the shorter leg has length , then the longer leg has length and the hypotenuse has length .

  8. Vocabulary

  9. 3 EXAMPLE Find an unknown side length of a right triangle Find the value for in the right triangle shown. SOLUTION Geometry Isosceles Conj.

  10. 4 EXAMPLE Use a calculator to solve a right triangle Solve . =20 SOLUTION

  11. 4 EXAMPLE Using indirect Measurement Hiking in Nepal You are hiking toward Machapuchare “Fish Tail” in the Annapurna range, but you reach a point where an avalanche has destroyed the trail (1). To avoid the avalanche, you take an alternative trail route. You turn onto a diagonal trail (2) that meets your original trail at a 48° angle and follow that trail for 3.6 miles until you hit another trail (3) that intersects back with your original trail at a 90° angle. How far were you from the intersection of your trail (1) and trail (3) when you turned onto the diagonal trail (2)? How far will you travel taking the alternative trail route around the avalanche? ≈ 2.4 mi You will travel ≈ 6.3 mi around the avalanche.

  12. 5 EXAMPLE Using Angle of Elevation KIS Flagpole You measure from a point on the ground 28 feet from the base of the KIS flagpole, the angle of elevation to the top of the flagpole is 63°. Estimate the height of the flagpole. SOLUTION The approximate height of the KIS flagpole is 55 feet.

  13. Lesson 9.1 Homework: • Practice B • Practice C “Honors”

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