Question

You use an extension ladder to repair a chimney that is 33 feet tall. For safety reasons you shouod always use an angle if about 75.5° between the ground and ladder. Your smallest ladder has a maximum length of 17 feet. You place the ladder 3 feet from the base of the chimney. How many feet long should the ladder be?

Answer 1

The length of the ladder is 34 ft

Explanation:

Extracting the key information from the question:-

*** The chimney to be repaired is 33ft tall.

*** The ladder to be used to repair the chimney must be at an angle of 75.5° with the ground.

*** The distance between the base of the chimney and the foot of the ladder is 3ft.

*** We are required to calculate the length of the ladder.

The shape that is formed as a result of the placement of the ladder on the wall of the chimney is a right angle triangle. We can calculate the length of this ladder using either Pythagoras theorem or the Sohcahtoa rule.

Pythagoras theorem:-

C^2 = A^2 + B^2

Where A = 33ft

B = 3ft

C^2 = 33^2 + 3^2

C^2 = 1089 + 9

C^2 = 1098

C = √1089

C = 34 ft

Sohcahtoa rule:-

Opposite/hypotenuse= sin y

Where opposite = 33 ft

hypotenuse = C (length of the ladder)

y = 75.5° (angle between the ladder and the ground).

33/C = sin 75.5°

33/C = 0.9681 (cross multiply)

C × 0.9681 = 33

C = 33/0.9681

C = 34 ft

Answer 2

Answer: The ladder should be at least 34 feet long (approximately)

Step-by-step explanation: Please refer to the diagram attached for details.

The chimney is depicted as line AB (33 ft). The distance from the base of the chimney to the ladder is depicted as line BC (3 ft). The ladder is placed such that it forms an angle of 75.5 degrees with the floor. Hence the required length of the ladder needed is shown in the diagram as line AC (line b). The resulting diagram now has an opposite (33 ft) and an hypotenuse (b) which is yet unknown.

To calculate line b, we shall apply the trigonometric ratio as follows;

SinC = opposite/hypotenuse

Sin 75.5 = 33/b

By cross multiplication we now have

b = 33/Sin 75.5

b = 33/0.9681

b = 34.087

Therefore the required length of the ladder is approximately 34 feet.