Math Problem Statement

For the right triangle shown, find cotA.

Solution

To find cotA\cot A in a right triangle, we can use the formula:

cotA=adjacent sideopposite side\cot A = \frac{\text{adjacent side}}{\text{opposite side}}

In this triangle:

  • The side adjacent to angle AA is 15.
  • The side opposite angle AA is 8.

Thus,

cotA=158\cot A = \frac{15}{8}

So, the value of cotA\cot A is 158\frac{15}{8} or 1.875 in decimal form.

Would you like more details or have any questions?


Here are some related questions for further exploration:

  1. How do we find other trigonometric ratios for angle AA in this triangle?
  2. What would cotA\cot A be if we only knew the hypotenuse and one side?
  3. How can we find angle AA using trigonometric functions?
  4. How is cotA\cot A related to tanA\tan A in terms of their values?
  5. Can we calculate cotA\cot A using other trigonometric identities?

Tip: Remember that cotθ=1tanθ\cot \theta = \frac{1}{\tan \theta}, so once you know tanθ\tan \theta, you can quickly find cotθ\cot \theta.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Right Triangle Ratios

Formulas

cot A = adjacent side / opposite side

Theorems

Definition of cotangent in a right triangle

Suitable Grade Level

Grade 9-10