Question

find the length of the altitude from w to $overline{uv}$ and the area of $\triangle uvw$. write your answer as an integer or as a decimal rounded to the nearest tenth. altitude = m area = m²

Explanation:

Step1: Find the altitude

We know that the altitude \(h\) from \(W\) to \(UV\) in \(\triangle UVW\) can be found using the sine - function. If we consider the side \(WV = 44\) m and the angle \(V=48^{\circ}\). The altitude \(h\) from \(W\) to \(UV\) is given by \(h = WV\sin V\).
\[h = 44\times\sin(48^{\circ})\]
\[h = 44\times0.743145\]
\[h\approx32.7\] m

Step2: Find the area of the triangle

The area of a triangle \(A=\frac{1}{2}\times base\times height\). Here, the base is \(UV = 46\) m and the height (altitude) \(h\approx32.7\) m.
\[A=\frac{1}{2}\times46\times32.7\]
\[A = 23\times32.7\]
\[A=752.1\] \(m^{2}\)

Answer:

Altitude = \(32.7\) m
Area = \(752.1\) \(m^{2}\)