Math Problem Statement

Label opp(30°), adj(30°), and hypotenuse clearly. Measure the length of opp(30°) and write it down.

Solution

In the given right triangle, we have two known angles: 30° and 60°. Here's how we can label the sides in relation to the 30° angle:

  1. Opposite (opp(30°)): This is the side opposite the 30° angle. In this case, it is the shorter leg of the right triangle.
  2. Adjacent (adj(30°)): This is the side adjacent to the 30° angle and forms part of the right angle. It is the longer leg of the right triangle.
  3. Hypotenuse: This is the longest side, opposite the 90° angle.

Labels:

  • The side opposite the 30° angle is opp(30°).
  • The side adjacent to the 30° angle is adj(30°).
  • The hypotenuse remains labeled as such.

Next Step: Measurement

  • To measure the length of opp(30°), you would need a ruler or specific measurements of the triangle.

If you have specific values or further questions, feel free to share. Would you like me to explain more or generate questions?


5 Related Questions:

  1. How do we calculate the length of the sides in a 30°-60°-90° triangle given the hypotenuse?
  2. What is the relationship between the sides in a 30°-60°-90° triangle?
  3. How can trigonometric functions help in finding the sides of the triangle?
  4. If the hypotenuse is 10 cm, what are the lengths of the other sides?
  5. How do we verify the Pythagorean theorem in this triangle?

Tip:

In a 30°-60°-90° triangle, the ratio of the sides is always 1:3:21 : \sqrt{3} : 2 (opposite 30°, adjacent to 30°, hypotenuse respectively).

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Right Triangle
Angle-Side Relationships

Formulas

Sine rule: sin(30°) = opp(30°) / hypotenuse
Pythagorean theorem: a^2 + b^2 = c^2

Theorems

30°-60°-90° Triangle Theorem

Suitable Grade Level

Grades 8-10