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A 24-foot ladder rests against a house near a second story window 20 feet from the ground. Assume that the ladder and the house both sit on level ground.
The measure of the angle formed by the base of the ladder and level ground is?
The measure of the angle formed by the top of the ladder and the second story window is?
The distance, on level ground, between the base of the ladder and the house is?



Answer :

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The measure of the angle formed by the base of the ladder and level ground is?

[tex] sin \alpha = \frac{cateto \ opposite}{cateto\ adjacent} \\ \\ sin \alpha = \frac{20}{24} \\ \\ sin \alpha =0.833 \\ \\ \alpha =sin^{-1} 0.833 \\ \\ \alpha =56.4^0[/tex]

The measure of the angle formed by the top of the ladder and the second story window is?
[tex]\alpha + \beta + 90^0=180 \\ \beta +56.4+90=180 \\ \beta =180-146.4 \\ \beta =33.6^0[/tex]

The distance, on level ground, between the base of the ladder and the house is?
Using Piagoras:

[tex]a^2+b^2=c^2 \\ a^2+20^2=24^2 \\ a^2+400=576 \\ a^2=576-400 \\ a^2=176 \\ a= \sqrt{176} \\ a=13.26 \ feet[/tex]

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Answer:

56

34

13

Step-by-step explanation:

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