Homework | Create a homework in a form of a quiz |

Which subject | Mathematics |

What age group | Year or Grade 6 |

What topic | trigonometry |

Question types | Open-ended |

Number of questions | 5 |

Number of answers | 4 |

Correct answers | Exactly 1 |

Show correct answers | |

Use images (descriptions) | |

Any other preferences |

Instructions: Answer the following questions to the best of your ability. Write down your answer to each question on a separate sheet of paper.

- What is trigonometry?
- Explain how to find the sine, cosine, and tangent of an angle in a right triangle.
- What is the Pythagorean theorem?
- Given a right triangle with legs of length 3 and 4, find the length of the hypotenuse.
- If the opposite side of an angle in a right triangle is 6 and the hypotenuse is 10, what is the sine of the angle?

Answers:

- Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.
- To find the sine, cosine, and tangent of an angle in a right triangle, you can divide the length of the opposite side, adjacent side, or hypotenuse by another side respectively.
- The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides (a²+b²=c²).
- Using the Pythagorean theorem, the length of the hypotenuse is sqrt(3²+4²) = 5.
- The sine of the angle is opposite/hypotenuse, which is 6/10 or 0.6.