The triangle △ABC is right-angled with right angle at corner C and angle α at corner A.

Question

The triangle △ABC is right-angled with right angle at corner C and angle α at corner A.Calculate the area of the triangle, given that c=|AB|=7, and that tan α=7/8.

Answer 1

There a several ways to proceed.

One such:

Let x and y be the lengths of the legs.

y/x=tan angle CAB=7/8

x²+y²=49.

Substitute and solve.