A parcel of land is in the shape of an isosceles triangle. The base has length 425 feet; the other sides, which are of equal length, meet at an angle of 39 degree. How long are the two equal side?
There are many approaches. Here are two:
Let the unknown sides be of length x.
Option 1. Drop a perpendicular from the vertex to the base and use the resulting right-triangle to solve for x:
$\displaystyle \sin (19.5^o) = \frac{212.5}{x} \, ......$
Option 2. Use the cosine rule to solve for x:
$\displaystyle 425^2 = x^2 + x^2 - 2(x)(x) \cos (39^o) \, ........$