Final answer:
B. 150 to 250 cm Using trigonometric functions, we calculate the permissible distances from the wall by taking the cosine of the minimum and maximum safe angles, 10 and 20 degrees respectively, then multiplying by the ladder’s length. The resulting base lengths give us the range of safe distances.
Step-by-step explanation:
The question asks for the permissible distances from the wall for a ladder with a certain angle range for safety. The ladder's length is 333 cm and the safe angle with the wall is between 10 and 20 degrees. To find the permissible distances, we can use trigonometric functions, specifically the cosine function since it relates the adjacent side to the hypotenuse in a right-angled triangle.For the minimum angle (10 degrees):The cosine of the minimum angle is θ = cos(10°).Using the ladder's length as the hypotenuse (H), we find the base (B) by B = H × cos(θ).For the maximum angle (20 degrees):
The cosine of the maximum angle is θ = cos(20°)Similarly, we find the base (B) for the maximum angle.After calculating the base distances for both angles using the ladder's length, we determine the range of permissible distances.To determine the permissible range of distances from the wall, we need to find the range of values for the length of the ladder segment that is in contact with the wall. This can be calculated using trigonometryLet x be the length of the ladder segment in contact with the wall. We can use the sine function to find x: sin(angle) = x/ladder lengthUsing the given angle range of 10 to 20 degrees, we can calculate the corresponding range of values for x. Plugging in the values, we find that x ranges from approximately 57.16 cm to 119.51 cm.