Math Problem Statement

Menentukan nilai x

Tentukan nilai cos θ dari gambar berikut!

Solution

The image shows a right-angled triangle with sides labeled. Let's identify the key details:

  • The triangle ABC\triangle ABC has:
    • AB=5AB = 5 (blue side, adjacent to angle θ\theta),
    • AC=3AC = 3 (red side, opposite angle θ\theta),
    • BC=7BC = 7 (hypotenuse).

The problem asks to find the value of cosθ\cos \theta, where θ\theta is the angle at vertex AA.

Solution:

The cosine of an angle θ\theta in a right triangle is given by: cosθ=adjacenthypotenuse\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}

Here:

  • The adjacent side is AB=5AB = 5,
  • The hypotenuse is BC=7BC = 7.

Thus: cosθ=57\cos \theta = \frac{5}{7}

The value of cosθ\cos \theta is 57\frac{5}{7}.

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

Here are some related questions:

  1. How do we calculate sinθ\sin \theta for this triangle?
  2. What is the value of tanθ\tan \theta?
  3. How can we verify the triangle's side lengths using the Pythagorean theorem?
  4. What is the significance of the angle θ\theta in trigonometry?
  5. Can we find the angle θ\theta using inverse cosine?

Tip: Always remember that in a right triangle, the cosine function relates the adjacent side to the hypotenuse!

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Right-Angled Triangles
Cosine

Formulas

cos θ = adjacent / hypotenuse

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 7-9