Question

Find the length of the perpendicular from the vertex opposite to the side $72$ m of the triangular field, whose other two sides are $30$ m and $78$ m.

Answer 1

Area of the triangle by using hero's rule
$=\sqrt{90(90-30)(90-72)(90-78)m^2}$
$=1080m^2$
$\therefore$ $AL=\frac{2Area}{base}=\frac{2\times 1080}{72}m$
$=30m$