Question

In the following right triangles, find the length of the unknown sides:​

Answer 1

GiveN:-

• AB = 15 cm.
• BC = 8 cm.
• Angle ABC = 90°.

To FinD:-

AC.

SolutioN:-

• As it is a right angle triangle we have to use the Pythagoras theorem to find the side AC.

So,

• AB = side
• BC = Base
• AC = Hypotenuse

By Pythagoras theorem,

$\large{\green{\underline{\boxed{\bf{(hypo)^2=(Base)^2+(Side)^2}}}}}$

where,

• Hypo = Hypotenuse = ?
• Base = 8 cm
• Side = 15 cm

Putting the values,

$\large\implies{\sf{(hypo)^2=(8)^2+(15)^2}}$

$\large\implies{\sf{(hypo)^2=64+225}}$

$\large\implies{\sf{(hypo)^2=289}}$

Square rooting both the sides,

$\large\implies{\sf{hypo=\sqrt{289}}}$

$\large\implies{\sf{hypo=\frac{+}{-}17.}}$

$\large\therefore\boxed{\bf{Hypotenuse=\frac{+}{-}17.}}$

VerificatioN:-

$\large\implies{\sf{(hypo)^2=(base)^2+(side)^2}}$

$\large\implies{\sf{(17)^2=(8)^2+(15)^2}}$

$\large\implies{\sf{289=64+225}}$

$\large\implies{\sf{289=289}}$

$\large\therefore\boxed{\bf{LHS=RHS}}$

So, the Hypotenuse (AC) is 17 cm.