Math Problem Statement

find teh act values of a and x in this diagram

Solution

This image shows a right-angled triangle with angles of 30° and 60°, and sides labeled aa and xx. The base is given as 20 cm. Let's find the actual values of aa and xx.

Step 1: Understand the triangle

This is a special right triangle, known as a 30°-60°-90° triangle. The properties of such triangles are:

  • The side opposite the 30° angle is half the hypotenuse.
  • The side opposite the 60° angle is 3/2\sqrt{3}/2 times the hypotenuse.

Given:

  • The angle opposite side xx is 60°.
  • The angle opposite side aa is 30°.
  • The base of 20 cm is the side opposite the 60° angle.

Step 2: Use the properties of the triangle

  1. Side xx: x=203201.73211.55 cmx = \frac{20}{\sqrt{3}} \approx \frac{20}{1.732} \approx 11.55 \text{ cm}

  2. Side aa:

    • Since aa is opposite the 30° angle, and using the property that the side opposite the 30° angle is half of the hypotenuse (which is 2020 cm): a=2×10=20 cma = 2 \times 10 = 20 \text{ cm}

Final Answer:

  • x11.55x \approx 11.55 cm
  • a=20a = 20 cm

Would you like any additional details, or do you have any questions?

Related Questions:

  1. How do the sides of a 45°-45°-90° triangle relate to each other?
  2. What is the general formula for the area of a right triangle?
  3. How do you find the hypotenuse in a right triangle given the other two sides?
  4. Can you use trigonometry to solve for unknown sides in any right triangle?
  5. What is the Pythagorean theorem and how is it applied?

Tip:

Remember that in a 30°-60°-90° triangle, the hypotenuse is always twice the length of the shorter leg.

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Math Problem Analysis

Mathematical Concepts

Geometry
Trigonometry
Special Right Triangles

Formulas

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Theorems

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Suitable Grade Level

Grades 10-12