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You are asked to calculate the angle \( \angle C \) of an isosceles triangle \( \triangle ABC \), where the height line \( CD \) is given, and the base \( AB \) is divided into two equal parts, each of length 3. The height \( CD = 5 \).

To find \( \angle C \), we can use trigonometry. Since triangle \( \triangle ACD \) is a right triangle, we can use the tangent function:
\[
\tan(\angle ACD) = \frac{\text{opposite}}{\text{adjacent}} = \frac{3}{5}
\]
Thus:
\[
\angle ACD = \arctan\left(\frac{3}{5}\right)
\]
\[
\angle C = 2 \times \angle ACD
\]
Calculating this gives:
\[
\angle ACD \approx 30.96^\circ
\]
\[
\angle C \approx 61.92^\circ
\]

Would you like a more detailed explanation?

1. How do you use tangent for angles in right triangles?
2. Why do we multiply \( \angle ACD \) by 2 to get \( \angle C \)?
3. What other trigonometric functions could help solve this?
4. How would the solution change if \( CD \) were longer?
5. Can we use the Pythagorean theorem to check the triangle dimensions?

**Tip:** Always remember to halve the base when using the height in isosceles triangles!

Given is an isosceles triangle ABC with a height line CD. Calculate angle C. The lengths of the two equal sides are 5, and the half of the base is 3.

Learn how to calculate the angle C of an isosceles triangle using trigonometric functions. The problem involves applying the tangent function and using the given side lengths of 5 and 3. Suitable for students in Grades 8-10.

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