Question

a ladder which is 4m long against a wall the bottom of the ladder is 1.5m from the bottom of the wall .how high up the wall does the ladder go?

Pls answer I know I said this billion times but first time doing a problem of Pythagoras the theorem ..

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Height\:of\:wall\approx3.7\:m}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given:}} \\ \tt: \implies Length \: of \: ladder = 4 \: m \\ \\ \tt: \implies Distance \: between \: wall \: and \: foot\: of \: ladder = 1.5 \: m \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Height \: of \: wall = ?$

• In the given question a ladder which is 4m long against a wall the bottom of the ladder is 1.5m from the bottom of the wall.

• We have to find height of wall at which ladder go.

• According to given question :

$\circ \: \tt{Consider \: a \: right \: \triangle \: ABC} \\ \\ \tt\circ \: 90 \degree \: at \: \angle \: C \\ \\ \tt\circ \:AB \: is \: the \: hypotenuse \\ \\ \tt\circ \: BC \: is \: the \: base \: \\ \\ \tt\circ \: AC \: is \: height \: of \:wall \\ \\ \bold{as \: we \: know \: that} \\ \tt: \implies {h}^{2} = {p}^{2} + {b}^{2} \: \: \: \: \: (By \: phythagoras \: theorem) \\ \\ \tt: \implies (AB)^{2} = {(AC)}^{2} + {(BC)}^{2} \\ \\ \tt: \implies {4}^{2} = {(AC)}^{2} + {1.5}^{2} \\ \\ \tt: \implies 16 = {(AC)}^{2} + 2.25 \\ \\ \tt: \implies 16 - 2.25 = {(AC)}^{2} \\ \\ \tt: \implies 13.75 = {(AC)}^{2} \\ \\ \tt: \implies AC= \sqrt{13.75} \\ \\ \green{\tt: \implies AC \approx 3.7\:m} \\ \\ \green{\tt\therefore height \: of \: pole \: is \: 3.7 \: m}$

Answer 2

$\huge{\tt{\pink{Hello!!!}}}$

$\tt{ \red{Acording \: to \: the \: question \: - \: }} \:$

$\tt{ \green{AB \: = \: distance \: from \: wall \: = \: 1.5m. \: }}$

$\tt{ \purple{BC \: = \: height \: of \: wall \: = \: h \: m. \: }}$

$\tt{ \pink{AC\: = \: length \: of \: ladder \: = \: 4m. \: }}$

$\huge{ \fbox{ \mathfrak{ \green{To \: \: find \: - \:BC }}}}$

$\tt{ \blue{ {AB}^{2} + \: {BC}^{2} \: = \: {AC}^{2} \: }}$

$\tt{ \pink{BC \: = 3.7m \: }}$

$</p><p>\huge{\tt{\purple{Hope \: This \: Helps !!! }}}$