Pythagoras Theorem

A ladder $50 \mathrm{d}\mathrm{m}$ long when set against the wall of a house just reaches a window at a height of $48 \mathrm{d}\mathrm{m}$. If the lower end of the ladder from the base of the wall is at the distance of $k \mathrm{dm}$, find the value of $k$.
 

The foot of a ladder is $6 \mathrm{m}$ away from a wall and its top reaches a window $8 \mathrm{m}$ above the ground. The ladder is shifted in such a way that its foot is $8 \mathrm{m}$ away from the wall. If the top of the ladder reaches a height of $H \mathrm{m}$, find the value of $H$.

Two poles of heights $6 \mathrm{m}$ and $11 \mathrm{m}$ stand on a plane ground. If the distance between their feet is $12 \mathrm{m}$. Find the distance between their tops.
 

A man goes $15 \mathrm{m}$ due west and then $8 \mathrm{m}$ due north. If he is at a distance of $k \mathrm{m}$ from the starting point, find the value of $k$.

The two legs of a right triangle are equal and the square of the hypotenuse is $50$. Find the length of each leg.

A ladder $3.7 \mathrm{m}$ long is placed against a wall in such a way that the foot of the ladder is $1.2 \mathrm{m}$ away from the wall. Find the height of the wall to which the ladder reaches in $\mathrm{m}$.

The hypotenuse of a triangle is $2.5 \mathrm{c}\mathrm{m}$. If one of the sides is $1.5 \mathrm{cm}$. Find the length of the other side in $\mathrm{cm}$.

In a right $△ABC$, the lengths of the legs are $a=2 \mathrm{c}\mathrm{m}, b=1.5 \mathrm{c}\mathrm{m}$. The length of the hypotenuse is $c \mathrm{cm}$, find the value of $c$.

In right $△\mathrm{ABC}$, the lengths of the legs are given as $a=3 \mathrm{c}\mathrm{m}, b=4 \mathrm{c}\mathrm{m}$. If the length of the hypotenuse is $c \mathrm{cm}$, then find the value of $c.$

In a right $△ABC$, the lengths of the legs are $a=8 \mathrm{c}\mathrm{m}, b=15 \mathrm{c}\mathrm{m}$. The length of the hypotenuse is $c \mathrm{cm}$, find the value of $c$.

 In right $△ABC$, the lengths of the legs are given. Find the length of the hypotenuse in $\mathrm{cm}$.
$a=6 \mathrm{c}\mathrm{m}, b=8 \mathrm{c}\mathrm{m}$

A $15 m$ long ladder is placed against a wall in such a way that the foot of the ladder is $9 m$ away from the wall. Up to what height does the ladder reach the wall?

The hypotenuse of a right triangle is $26 \mathrm{cm}$ long. If one of the remaining two sides is $10 \mathrm{cm}$ long, the length of the other side is

A ladder is placed in such a way that its foot is $15 m$ away from the wall and its top reaches a window $20 m$ above the ground. The length of the ladder is

Two poles of heights $6 m$ and $11 m$ stand vertically on a plane ground. If the distance between their feet is $12 m$, the distance between their tops is

If $∆ABC$ is an isosceles right-triangle right-angled at $C$ such that $AC=5 \mathrm{cm}$, then,$AB=$

$∆ABC$ is a right-triangle right-angled at A. If $AB=24 \mathrm{cm}$ and $AC=7 \mathrm{cm}$ then, $BC=$

Which of the following is/are not Pythagorean triplet(S)?

Draw a triangle $ABC$, with $AC = 4 cm, BC=3 cm$and $\angle C=80°$. Measure $AB$. Is $A{B}^2=(AC{)}^2+(BC{)}^2$? If not which one of the following is true: $(AB{)}^2>(AC{)}^2+(BC{)}^{2}or (AB{)}^2<(AC{)}^2+(BC{)}^2?$

Draw a triangle $ABC$, with $AC= 4 cm, BC= 3 cm$ and $\angle C=105°$. Measure $AB$. Is $A{B}^2=(AC{)}^2+(BC){ }^2$? If not which one of the following is true: $(AB{)}^2>(AC{)}^2+\left(BC\right){ }^2$ or $(AB{)}^2<(AC{)}^2+(BC{)}^2$?