Calculate the angle gamma in the triangle 'c'.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Calculate the angle $\gamma$ in the triangle 'c'.
In the right-angled triangle 'c', the side adjacent to angle $\gamma$ is 6, and the hypotenuse is 15. We use the cosine function.
$$ \cos(\gamma) = \frac{\text{adjacent}}{\text{hypotenuse}} $$
$$ \cos(\gamma) = \frac{6}{15} $$
$$ \cos(\gamma) = 0.4 $$
To find $\gamma$, we take the inverse cosine:
$$ \gamma = \arccos(0.4) $$
$$ \gamma \approx 66.4218^\circ $$
Rounding to the nearest 0.1 degree:
$$ \gamma \approx \boxed{66.4^\circ} $$
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