To find the length of side \( a \), we can use the sine function from trigonometry. In a right triangle, the sine of an angle is defined as the opposite side over the hypotenuse.
Given:
- \( h = 10 \) meters (this is the hypotenuse)
- \( m∠C = 39° \) (this is one of the angles in the right triangle)
We can use the sine function as follows:
\[ \sin(39°) = \frac{a}{h} \]
Substituting the known values:
\[ \sin(39°) = \frac{a}{10} \]
Now, solve for \( a \):
\[ a = 10 \cdot \sin(39°) \]
Using a calculator to find \( \sin(39°) \):
\[ \sin(39°) \approx 0.6293 \]
Now substitute this value into the equation for \( a \):
\[ a = 10 \cdot 0.6293 \approx 6.293 \]
Rounding to the nearest whole number, we find:
\[ a \approx 6 \text{ meters} \]
Thus, the length of side \( a \) is approximately 6 meters.
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