University:
High School
Course:
High School Mathematics
Academic year:

2022
Views:

453

Pages:

6
Author:

hanzestisswj

Certainly, here's the breakdown of the image you provided: Title: Study Guide Geometry 9.1 The Pythagorean Theorem For any right triangle: a² + b² = c² You have a triangle if: Small + middle > big a² + b² < c² makes an obtuse triangle a² + b² = c² makes an acute triangle Solve for the variable: Diagram: A right triangle with sides labeled 10, 6, and x. 6² + x² = 10² 36 + x² = 100 x² = 64 x = 8 Diagram: A right triangle with sides labeled 7, 8, and c. 7² + 8² = c² 49 + 64 = c² 113 = c² √113 = c Decide if the numbers make a triangle. If so, classify it. 6, 2, 5 2 + 5 = 7 > 6 Triangle 10, 6, 3 3 + 6 = 9 < 10 Not a triangle 3, 4, 5 3 + 4 = 7 > 5 Triangle 3² + 4² = 5² 9 + 16 = 25 25 = 25 Right triangle 9.2 Special Right Triangles Place your "w" Diagrams of 45-45-90 and 30-60-90 triangles with side lengths labeled in terms of "w". Solve the one side and use it for the others Solve for the variables. Diagram: A 45-45-90 triangle with one leg labeled 5. a = w b = w√2 a = 5 b = 5√2 Diagram: A 30-60-90 triangle with the hypotenuse labeled 9√3. d = 2w c = w√3 c = 9√3 d = 2w = 18 If the legs of a square equal 6, what is the length of the diagonal? Diagonal = w√2 Diagonal = 6√2 9.3 Similar Right Triangles Content: Geometric Mean: "P" is the geometric mean for 9 and 12. P² = 9 * 12 P² = 108 P = 6√3 Complete the proportions using the picture: Several right triangles are shown with labeled sides. Proportions are set up using the relationships between the sides of the triangles. Find the variables: 5) x²/5 = 9/x x² = 45 x = √45 = 3√5 6) 12y = 18² y = 18²/12 = 27 7) 27/z = z/16 z² = 27 * 16 z = √432 = 12√3 9.4 The Tangent Ratio Content: For any right triangle: Tangent of an angle = opposite side / adjacent side tan A = opp / adj Solve for x. (answers in trig and decimal form) Diagram: A right triangle with angles labeled 41° and 49°, and sides labeled 12 and x. x * tan 41° = 12 x = 12 / tan 41° x = 13.8 Diagram: A right triangle with angles labeled 27° and 63°, and sides labeled 15 and x. 15 * tan 27° = x x = 7.6 Diagram: A right triangle with angles labeled x and 18°, and sides labeled 12 and 18. tan x = 18 / 12 x = tan⁻¹(3/2) x = 56.3° Write the tangent ratio for ∠A and ∠B Diagram: A right triangle with angles labeled A and B, and sides labeled 20, 52, and 48. tan A = 48 / 20 tan B = 20 / 48 A ladder that is 15 feet long is leaning against a wall. The ladder needs to make a 70° angle of elevation to be safe. How far away from the wall is the ladder? Diagram: A right triangle with the hypotenuse (ladder) labeled 15 feet, the angle of elevation labeled 70°, and the base (distance from the wall) labeled x. cos 70° = x / 15 15 * cos 70° = x 5.14 = x Ladder needs to be 5.14 feet away from the wall.