Math Problem Statement

Selvitä kulman α suuruus. Anna vastaus asteina ilman astemerkkiä. Pyöristä vastaus kymmenenosien tarkkuudelle.

Solution

To calculate the angle α\alpha, we use the trigonometric ratios given in the diagram. Since the adjacent side is 9.89.8 and the hypotenuse is 12.612.6, we can use the cosine function:

cosα=adjacenthypotenuse=9.812.6\cos \alpha = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{9.8}{12.6}

First, calculate 9.812.6\frac{9.8}{12.6}:

9.812.60.7778\frac{9.8}{12.6} \approx 0.7778

Now find α\alpha using the inverse cosine function:

α=cos1(0.7778)\alpha = \cos^{-1}(0.7778)

Using a calculator:

α38.5\alpha \approx 38.5^\circ

So, the angle α\alpha is approximately 38.538.5^\circ.

Let me know if you have questions or need a detailed breakdown of any step! Here are some related questions for practice:

  1. How would you calculate α\alpha using the sine or tangent functions?
  2. What is the value of sinα\sin \alpha and tanα\tan \alpha?
  3. How can you verify this result using Pythagoras' theorem?
  4. What is the complementary angle of α\alpha in this triangle?
  5. 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