Question

In a house that is being renovated, two corridors meet at right angles as shown in the diagram. Workmen attempting to take a ladder around the corner get the ladder stuck when it is at an angle of 45 degrees to each wall.



a) Determine the length of the ladder

b) Determine the length of a second ladder that got stuck when it was at angle of 600 with the wall of the one meter corridor.

Answer 1

Answer:pls check the answer in the attachment

Step-by-step explanation:

Answer 2

a) length of ladder is 3√2 m

b) length of ladder is (12 + 2√3)/3 m

a)

In triangle ABC

<BAC = 45°

AB = 2m

Cos 45° = B / H= AB/AC

1/√2 = 2/AC

AC = 2√2 m

In triangle DFC

<DFC = 45°

DF = 1m

Cos 45° = B / H= DF/CF

1/√2 = 1/CF

CF = √2 m

length of ladder = AC + CF

length of ladder = 2√2+√2

length of ladder = 3√2

b)

In triangle ABC

<BAC = 60°

AB = 2m

Cos 60° = B / H= AB/AC

1/2 = 2/AC

AC = 4 m

In triangle DFC

<DFC = 30°

DF = 1m

Cos 30° = B / H= DF/CF

√3/2 = 1/CF

CF = 2/√3 m

length of ladder = AC + CF

length of ladder = 4+2/√3

length of ladder = (4√3 + 2)/√3

length of ladder = (12 + 2√3)/3 m