Question

The lengths of two sides of the right triangle ABC shown in the illustration given a= 15in and c= 25in

Answer 1

Since the triangle is a right angled triangle, Pythagoras Theorem must be satisfied.

From the diagram, it is observed that 'c' is the hypotenuse, and 'a' and 'b' are the legs.

Then the Pythagoras Theorem becomes,

$c^2=a^2+b^2$

Substitute the given values,

$\begin{gathered} 25^2=15^2+b^2 \\ 625=225+b^2 \\ b^2=625-225 \\ b^2=400 \end{gathered}$

Taking square roots on both sides of the equation,

$\begin{gathered} b=\sqrt[]{400} \\ b=20 \end{gathered}$

Note that we have neglected the negative value '-20' for 'b' since the side of a triangle cannot be negative.

Thus, the side 'b' is 20 inches.