Question

An 8.50 m long ladder leans against the side of a building. The ladder is initially inclined at an angle of 47.0° to the horizontal. The base of the ladder is then moved 0.82 m closer to the building. At what angle is the ladder now inclined with respect to the horizonta

Answer 1

The angle of the ladder inclined with respect to the horizontal after being moved a distance of 0.82 m closer to the building is 53.84°

cos θ = Adjacent side / Hypotenuse

θ$_{1}$ = 47°

Hypotenuse = Length of ladder = 8.5 m

cos 47° = Adjacent side / 8.5

Adjacent side = Initial distance of base of ladder from the building = 5.8 m

Adjacent side 2 = Final distance of base of ladder from the building

Adjacent side 2 = 5.8 - 0.82 = 4.98 m

cos θ$_{2}$ = Adjacent side 2 / Hypotenuse

cos θ$_{2}$ = 4.98 / 8.5 = 0.59

θ$_{2}$ = $cos^{-1}$ ( 0.59 )

θ$_{2}$ = 53.84°

The formula used above is one of trigonometric ratios. Trigonometric ratios can used only in a right angled triangle where one of the angles in at 90 degrees and the other two angles are less than 90 degrees.

Therefore, the angle of the ladder inclined with respect to the horizontal after being moved is 53.84°

To know more about trigonometric ratios

brainly.com/question/1201366

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