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 and . The base is given as 20 cm. Let's find the actual values of and .
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 times the hypotenuse.
Given:
- The angle opposite side is 60°.
- The angle opposite side is 30°.
- The base of 20 cm is the side opposite the 60° angle.
Step 2: Use the properties of the triangle
-
Side :
-
Side :
- Since is opposite the 30° angle, and using the property that the side opposite the 30° angle is half of the hypotenuse (which is cm):
Final Answer:
- cm
- cm
Would you like any additional details, or do you have any questions?
Related Questions:
- How do the sides of a 45°-45°-90° triangle relate to each other?
- What is the general formula for the area of a right triangle?
- How do you find the hypotenuse in a right triangle given the other two sides?
- Can you use trigonometry to solve for unknown sides in any right triangle?
- 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.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Geometry
Trigonometry
Special Right Triangles
Formulas
-
Theorems
-
Suitable Grade Level
Grades 10-12