Math Problem Statement
Selvitä kulman α suuruus. Anna vastaus asteina ilman astemerkkiä. Pyöristä vastaus kymmenenosien tarkkuudelle.
Solution
To calculate the angle , we use the trigonometric ratios given in the diagram. Since the adjacent side is and the hypotenuse is , we can use the cosine function:
First, calculate :
Now find using the inverse cosine function:
Using a calculator:
So, the angle is approximately .
Let me know if you have questions or need a detailed breakdown of any step! Here are some related questions for practice:
- How would you calculate using the sine or tangent functions?
- What is the value of and ?
- How can you verify this result using Pythagoras' theorem?
- What is the complementary angle of in this triangle?
- How would you write the result in radians instead of degrees?
Tip: Always double-check if you're in degree mode when solving trigonometric problems with angles in degrees!
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Right Triangle Geometry
Angles
Formulas
cos α = adjacent / hypotenuse
α = cos⁻¹(value)
Theorems
Trigonometric Ratios
Suitable Grade Level
Grades 9-11