Find the exact value of cosine, AcosA in simplest radical form.

A
B
C
6
7
√85

It seems like you are asking to find the exact value of \(\cos A\) in simplest radical form. You provided some additional information which seems to be the lengths of the sides of a triangle, possibly a right triangle:

- Side opposite angle \(A\): \(6\)
- Side adjacent to angle \(A\): \(7\)
- Hypotenuse: \(\sqrt{85}\)

### Step-by-step solution:

1. **Identify the cosine formula**: In a right triangle, the cosine of an angle \(A\) is defined as:
   \[
   \cos A = \frac{\text{Adjacent side}}{\text{Hypotenuse}}
   \]

2. **Apply the values**:
   \[
   \cos A = \frac{7}{\sqrt{85}}
   \]

3. **Rationalize the denominator**: To simplify the expression, multiply the numerator and the denominator by \(\sqrt{85}\):
   \[
   \cos A = \frac{7}{\sqrt{85}} \times \frac{\sqrt{85}}{\sqrt{85}} = \frac{7\sqrt{85}}{85}
   \]

Thus, the exact value of \(\cos A\) in simplest radical form is:
\[
\boxed{\frac{7\sqrt{85}}{85}}
\]

Would you like more details on this solution or further clarification?

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Here are 5 related questions to expand your understanding:
1. How would you find the sine of angle \(A\) using the given triangle?
2. What is the exact value of the tangent of angle \(A\) in simplest form?
3. How can you find the angle \(A\) using inverse trigonometric functions?
4. What is the Pythagorean theorem, and how is it used to verify the hypotenuse?
5. What is the significance of rationalizing the denominator?

**Tip**: Always verify that the triangle you are working with follows the Pythagorean theorem when dealing with right triangles.

Find the exact value of cosine, AcosA in simplest radical form. A B C 6 7 √85

Discover how to find the exact value of cosine A in simplest radical form for a right triangle with sides 6, 7, and √85. Learn key trigonometry concepts like the cosine formula and rationalizing the denominator. This problem is ideal for students in Grades 9-11.

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