Geometry Chapter 9 Quiz

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Questions and Answers

What do special right triangles refer to?

  • Triangles with obtuse angles
  • 45-45-90 and 30-60-90 triangles (correct)
  • Triangles with equal sides
  • Isosceles triangles

How do you find the hypotenuse in a 45-45-90 triangle?

hypotenuse = leg x √2

How do you find the hypotenuse in a 30-60-90 triangle?

hypotenuse = shortest leg x 2

How do you find the longest leg of a 30-60-90 triangle?

<p>longest leg = shortest leg x √3</p> Signup and view all the answers

What is Theorem 9.8 (45-45-90 Theorem)?

<p>In a 45-45-90 triangle, the hypotenuse is √2 times as long as each leg.</p> Signup and view all the answers

What is Theorem 9.9 (30-60-90 Theorem)?

<p>In a 30-60-90 triangle, the hypotenuse is twice as long as the shortest leg and the longer leg is √3 times as long.</p> Signup and view all the answers

What are trigonometric ratios?

<p>Ratios that help solve side lengths of right triangles.</p> Signup and view all the answers

What does SOHCAHTOA stand for?

<p>SIN/sine (Opposite/Hypotenuse), COS/cosine (Adjacent/Hypotenuse), TAN/tangent (Opposite/Adjacent)</p> Signup and view all the answers

What does it mean to solve a right triangle?

<p>The process of determining all 6 measurements within a right triangle (3 side lengths, 3 angle measures).</p> Signup and view all the answers

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Study Notes

Special Right Triangles

  • Includes two types of triangles: 45-45-90 and 30-60-90.
  • Known for consistent relationships among their side lengths.

45-45-90 Triangle

  • Hypotenuse can be calculated using the formula: hypotenuse = leg x √2.

30-60-90 Triangle

  • Hypotenuse is found using: hypotenuse = shortest leg x 2.
  • The longest leg (2nd longest side) can be determined as: longest leg = shortest leg x √3.

Theorems

  • Theorem 9.8 (45-45-90 Theorem): In this triangle, the hypotenuse measures √2 times the length of each leg.
  • Theorem 9.9 (30-60-90 Theorem): In this triangle, the hypotenuse is twice the length of the shortest leg, while the longer leg equals √3 times the shortest leg.

Trigonometric Ratios

  • Essential for calculating side lengths in right triangles.

SOHCAHTOA

  • A mnemonic to remember trigonometric functions:
    • SIN (sine): Opposite/Hypotenuse
    • COS (cosine): Adjacent/Hypotenuse
    • TAN (tangent): Opposite/Adjacent

Solving a Right Triangle

  • Involves calculating all six measurements: three side lengths and three angle measures.

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