Chapter 8 Right Triangles and Trigonometry Pythagorean Theorem
- Slides: 28
Chapter 8 Right Triangles and Trigonometry
Pythagorean Theorem • Pythagorean Theorem: In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse • Formula: ______________ c a b
Objective 1(a) • Use the Pythagorean theorem to solve for the missing sides of the triangle.
Classifying triangles as acute or obtuse • Theorem 8 -3: If the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the other two sides, then the triangle is _________. • If c 2 > a 2 + b 2 • Theorem 8 -4: If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, then the triangle is _________. • If c 2 < a 2 + b 2
Objective 1(b) •
Practice: pp. 496 -497 #22, 29 -32, 36 -38
Special Right Triangles • 45 -45 -90 Triangle • The two legs are ________. • To find the hypotenuse, multiply the length of the leg by ______.
Objective 2(a) • The triangles below are isosceles right triangles. Find the missing side lengths. y 5 x 10 x y
Special Right Triangles • 30 -60 -90 Triangle • To find the hypotenuse, multiply the ________ by _______. • To find the long leg, multiply the ________ by _____.
Objective 2(b) • The triangles below are 30 -60 -90 triangles y 2 10 x y x 6
Practice: pp. 503 -504 #7 -12, 15 -20, 23 -28
Trigonometry – Trigonometric Ratios • B c a C b A
Objective 3(a) • Write the sine, cosine, and tangent ratios for G • Sin G = • Cos G = • Tan G = • Use a trigonometric ratio to solve for w.
Trigonometry – Using Inverses •
Objective 3(b) • Use a trig ratio to solve for x. • Use a trig ratio to solve for P.
Practice: pp. 510 -511 #11 -19, 22 -27, 33 -35
Law of Sines • The law of sines relates the sine of each angle to the length of the opposite side. A c b C a B
Objective 5(a) • Solve each triangle.
Practice: p. 525 #6 -11
Law of Cosines • The law of cosines relates the cosine of each angle to the side lengths of the triangle. a 2 = A b 2 = c b c 2 = C a B
Objective 6(a) • Solve each triangle.
Practice: pp. 530 -531 #7, 8, 11, 13, 19 -22