A ladder that is 20 ft. Long is leaning against the side of a building. If the angle formed between the ladder and the ground is

Question

3 years ago

14

75, how far is the bottom of the ladder from the base of the building?

1 answer:

nexus9112 [7] · Answer 1 · 2022-05-18T12:10:44+03:00

Answer:

The ladder from the base of the building is 5.18 ft (Approx)

Step-by-step explanation:

As given

A ladder that is 20 ft. Long is leaning against the side of a building.

If the angle formed between the ladder and the ground is 75.

Now using the trignometric property .

$cos\theta = \frac{Base}{Hypotenuse}$

As shown in the figure.

$\theta = 75^{\circ}$

Base = CB

Hypotenuse = AC = 20 ft.

Put in the trignometric identity .

$cos75^{\circ} = \frac{CB}{AC}$

$cos75^{\circ} = \frac{CB}{20}$

$cos\ 75^{\circ} = 0.259$

Put in the above

$0.259= \frac{CB}{20}$

$0.259 = \frac{CB}{20}$

CB = 0.259 × 20

CB = 5.18 ft (Approx)

Therefore the ladder from the base of the building is 5.18 ft (Approx) .