To find the length of side \( a \) in the triangle where \( h = 10 \) meters and \( m∠C = 39° \), we can use trigonometric functions. Assuming the context is that \( h \) represents the height from vertex C to side \( a \), we can use the sine function:
\[ \sin(∠C) = \frac{\text{opposite}}{\text{hypotenuse}} \]
In this case, the opposite side is the height \( h \) and the hypotenuse is the length of the side \( a \). We can express this as:
\[ \sin(39°) = \frac{h}{a} \]
Substituting in the known value of \( h \):
\[ \sin(39°) = \frac{10}{a} \]
Rearranging gives us:
\[ a = \frac{10}{\sin(39°)} \]
Now, calculating \( \sin(39°) \):
\[ \sin(39°) \approx 0.6293 \]
Now we can substitute this value into the equation for \( a \):
\[ a \approx \frac{10}{0.6293} \approx 15.9 \text{ meters} \]
Rounding to the nearest whole number gives us:
\[ a \approx 16 \text{ meters} \]
So the length of side \( a \) is approximately 16 meters.
3 answers