Math Problem Statement
Solution
To solve the right triangle, the given data includes:
- Angle
- Side (the side opposite angle ).
Goal:
Find:
- The hypotenuse ().
- The other leg ().
- The remaining angle ().
Solution:
-
Find the remaining angle : In a right triangle, the sum of the angles is . Therefore:
-
Find the hypotenuse : Using the sine function: Substituting:
-
Find the other leg : Using the tangent function: Substituting:
Final Answer:
Would you like further explanations on any of these steps?
Here are 5 questions you could explore:
- What are the primary trigonometric ratios, and how are they applied in right triangles?
- Can this method work for non-right triangles? Why or why not?
- How would the calculations change if side was given instead of side ?
- What tools can simplify solving trigonometric problems in real life?
- How do you verify that your solutions are correct in problems like these?
Tip: When solving for a triangle's missing sides or angles, always confirm that the relationships between the sides and angles satisfy the Pythagorean theorem and the sum of angles rule!
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Right Triangles
Angle Sum Property
Formulas
A = 90° - B
c = a / sin(B)
b = a / tan(B)
Theorems
Angle Sum Property in Triangles
Trigonometric Ratios: Sine and Tangent
Suitable Grade Level
Grades 9-12