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A 20 foot ladder rests against the top of a 15 foot building. How far does the ladder extend from the base of the wall and what angle does the ladder make with the ground?

Respuesta :

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Look at the picture.

Calculate x using the Pythagorean theorem:
[tex]x^2+15^2=20^2 \\ x^2+225=400 \\ x^2=400-225 \\ x^2=175 \\ x=\sqrt{175} \\ x=\sqrt{25 \times 7} \\ x=5\sqrt{7} \\ x \approx 13.23[/tex]

Calculate α using sine:
[tex]\sin \alpha =\frac{15}{20} \\ \sin \alpha= 0.7500 \\ \alpha \approx 49^\circ[/tex]

The ladder extends approximately 13.23 feet (exactly: 5√7 feet) from the base of the wall and makes an approximately 49° angle with the ground.
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