A 6-meter long ladder is leaning against a wall. if the top of the ladder makes an angel of 45\xb0 with the wall, how far is the foot of the ladder from the wall?



A 6-meter long ladder is leaning against a wall. if the top of the ladder makes an angel of 45° with the wall, how far is the foot of the ladder from the wall?​

LADDER LEANING WALL

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» As the 6-meter ladder leans at the wall, it creates a 45° angle on the top most between the ladder and the wall. Lets represent the sides and angles as variables; Angle A as the top most, angle C as the bottom most, angle B as the placement of the wall on the ground, (b) as the measure of the ladder, (c) as the height of the wall, and (a) as the distance from the foot of ladder to the wall.

» Since angle A was the given measure of an angle, that would be our reference on choosing a trigonometric ratio. A six-meter ladder (b) refers as the hypothenuse and (a) was the distance we were finding. Side (a) is the opposite side of our reference. Well since the opposite side and the hypothenuse are present on angle A, we will gonna use the sine ratio (sin).

 \:  :  \implies \sf \large sin  \: \theta =  \frac{opposite \: side}{hypotenuse}

\implies \sf \large sin  \:A  =\frac{a}{b}

\implies \sf \large sin  \:45 \degree =\frac{a}{6m}

\implies \sf \large a = 6m(sin \: 45 \degree)

\implies \sf \large a =4.24m

Final Answer:

 \tt \huge» \:  \purple{4.24 \: meters}

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