Math Problem Statement

Can u help me solve this equation?

Solution

The image shows a trigonometry problem involving a right triangle. The task is to find the value of tan45\tan 45^\circ.

Solution:

In a right triangle, the tangent of an angle is given by the ratio of the opposite side to the adjacent side:

tanθ=oppositeadjacent\tan \theta = \frac{\text{opposite}}{\text{adjacent}}

For θ=45\theta = 45^\circ, we have:

tan45=oppositeadjacent=1\tan 45^\circ = \frac{\text{opposite}}{\text{adjacent}} = 1

This is because, in a 45-degree right triangle, the opposite and adjacent sides are equal, making their ratio equal to 1.

Answer:

tan45=1\tan 45^\circ = 1

Would you like more details or have any questions?

Related Questions:

  1. What is the value of tan30\tan 30^\circ?
  2. How does the tangent function relate to the unit circle?
  3. What is the general formula for the tangent of an angle in terms of sine and cosine?
  4. What are the values of tan\tan at 00^\circ, 9090^\circ, and 180180^\circ?
  5. Can you explain how to derive the tangent values for special angles (30°, 45°, 60°)?

Tip:

For any angle θ\theta, tanθ\tan \theta can also be calculated using sinθcosθ\frac{\sin \theta}{\cos \theta}.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Right Triangle

Formulas

Tangent of an angle in a right triangle

Theorems

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Suitable Grade Level

High School