Answer to Question #279782 in Trigonometry for Micheal

Question

Marco would like to hang a banner over his shoe store. He has two ladders and would like to know high above the ground each ladder will allow him to place the banner.

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

The 15-foot ladder makes a ________ degree angle with the building.

Explain and show the work you used to solve the problem. Justify the answer you have.

Will the 13-foot ladder make the same angle with the building? Justify your reasoning.

Answer 1

Let x be the angle between the 13ft ladder and the ground

Then $\sin x = \dfrac{11.3}{13} = 0.8692$

$x= 60.37°$

So $\sin 60.37 = \dfrac{y}{15}$

$y = 13$ ft to the nearest tenth

Let z be the angle between the ladder and the wall.

Then $\cos z = \dfrac{11.3}{13} = 0.8692$

$z =$ $29.63°$

So $\cos 29.63 = \dfrac{p}{15}$

$p = 13$ ft to the nearest tenth

So 29.63° is the angle it makes with the building. The solution was derived while trying to get the distance between the point the ladder touches the wall and the ground

Yes. This is because $\cos z = \dfrac{11.3}{13} = \dfrac{13}{15}$