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. Let's 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).
[tex] \: : \implies \sf \large sin \: \theta = \frac{opposite \: side}{hypotenuse} [/tex]
[tex]\implies \sf \large sin \:A =\frac{a}{b} [/tex]
[tex]\implies \sf \large sin \:45 \degree =\frac{a}{6m} [/tex]
[tex]\implies \sf \large a = 6m(sin \: 45 \degree)[/tex]
[tex]\implies \sf \large a =4.24m[/tex]
Final Answer:
[tex] \tt \huge» \: \purple{4.24 \: meters}[/tex]
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