Question #280146

His 13- foot ladder leans against the building at a point that is 11.3 feet above the ground.





At what height would a 15-foot ladder touch the building if both ladders form the same angle with the ground? Round your answer to the nearest tenth.





____________ feet







A 15-foot ladder leaning up against a wall at the same angle as the 13-foot ladder would touch the wall at _______ feet.





Explain how you determined your answer (explain all work used to determine the answer).







Find the angle that the 15-foot ladder makes with the building. Round your answer to the nearest tenth. ____________ degrees

1
Expert's answer
2021-12-16T15:05:27-0500
sinα=hl=HL=>H=Llh\sin \alpha=\dfrac{h}{l}=\dfrac{H}{L}=>H=\dfrac{L}{l}\cdot h

H=151311.313.0 (ft)H=\dfrac{15}{13}\cdot 11.3\approx13.0\ (ft)

13.0 feet.


A 15-foot ladder leaning up against a wall at the same angle as the 13-foot ladder would touch the wall at 13.013.0 feet.



cosβ=11.313,0<α<90°\cos \beta=\dfrac{11.3}{13}, 0<\alpha<90\degree

β=cos1(11.3/30)29.6°\beta=\cos^{-1}(11.3/30)\approx29.6\degree

The angle that the 15-foot ladder makes with the building is 29.6°.29.6\degree.



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