Answer to Question #279775 in Algebra 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.

Question 1

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 

Question 2

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). Justify your answer.

Question 3

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

____________ degrees

Question 4

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.

Answer 1

Question 1

Angle formed by the 13- foot ladder and the ground is $sin^{-1}(11.3/13)=60.4^0$

The height a 15-foot ladder would touch the building, $h/15=sin60.4^0$

$h=15\times sin60.4^0=13.0feet$

Question 2

A 15-foot ladder leaning up against a wall at the same angle as the 13-foot ladder would touch the wall at _13.0______ feet.

Explanation:

The 13-foot ladder forms a right-angled triangle with the wall.

angle formed at the ground is sine inverse of opposite side(11.3) divided by hypotenuse(13).

Angle formed by the 13- foot ladder and the ground is $sin^{-1}(11.3/13)=60.4^0$

The same approach can be used for the 15-foot ladder where sine of $60.4^0=opp/hyp=h/15$

Hence;

$h=15\times sin60.4^0=13.0feet$

Question 3

The angle that the 15-foot ladder makes with the building $=cos^{-1}(13/15)=29.9^0$

Question 4

The 15-foot ladder makes a ___$29.9^0$ _____ degree angle with the building.

Explanation:

Use the ladder as the hypotenuse and the height from the ground to the tip of the ladder as the adjacent side.

This gives $cos^{-1}(13/15)=29.9^0$

Note $Cos \theta= adj/hyp$