Question

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

Answer 1

Distance between ladder and base of the wall is
`5√(7)` foot.

Angle of ladder make with the ground is about
`48.59^\circ`.

Explanation:

From the given information,

Length of ladder = 20 foot

Height of building = 15 feet

We need to find the distance between ladder and base of the wall.

We know that wall is perpendicular to floor. It means ladder is hypotenuse.

Using Pythagoras theorem, we get

`hypotenuse^2=base^2+perpendicular^2`

`(20)^2=base^2+(15)^2`

`400-225=base^2`

`√(175)=base`

`5√(7)=base`

Therefore, the distance between ladder and base of the wall is
`5√(7)` foot.

In a right angle triangle,

`\sin \theta=(perpendicular)/(Hypotenuse)`

`\theta=\sin^(-1)\left((15)/(20)\right)`

`\theta \approx 48.59^\circ`

Therefore, the angle of ladder make with the ground is about
`48.59^\circ`.

Answer 2

Recognise firstly that you're making a right-angled triangle, with the hypotenuse being the ladder; and the wall and ground making up the other two sides. One vertical side is 15 ft long, the hypotenuse is 20 ft long. Use Pythagoras' Theorem to solve for the length of the remaining side: a2+b2=c2152+b2=202b2=400−225b2=175b=175−−−√=13.22ft To get the angle the ladder makes to the ground, use the trigonometric functions - sine in this case: sinθ=oppositehypotenusesinθ=1520θ=sin−1(0.75)θ=0.848radians(48.5degrees)