we know that
The area of a right triangle is equal to
[tex] Area=\frac{1}{2} (Leg1*Leg2) [/tex]
In this problem
[tex] Leg\ 1=27.6\ cm \\ Hypotenuse=30\ cm\\ Leg\ 2=? [/tex]
Applying the Pythagorean Theorem
[tex] Hypotenuse^{2} =Leg\ 1^{2} +Leg\ 2^{2} \\ Leg\ 2^{2}=Hypotenuse^{2}-Leg\ 1^{2}\\ Leg\ 2^{2}=30^{2} -27.6^{2} \\ Leg\ 2^{2}=138.24\\ Leg\ 2=11.76\ cm [/tex]
Find the area
[tex] Area=\frac{1}{2} (27.6*11.76) [/tex]
[tex] Area=162.29\ cm^{2} [/tex]
therefore
the answer is
the approximate area of the triangle is [tex] 162.29\ cm^{2} [/tex]
