Question

A ladder 9.00 m long leans against the side of a building. if the ladder is inclined at an angle of 75.0° to the horizontal, what is the horizontal distance from the bottom of the ladder to the building?

Answer 1

The horizontal distance from the bottom of the ladder to the building is approximately 2.33 meters, calculated using the cosine of the inclination angle (75°) multiplied by the length of the ladder (9.00 m).

Step-by-step explanation:

The student's question is asking about finding the horizontal distance from the base of a ladder to a building when the ladder is inclined at a certain angle. To find this distance, we can use trigonometry, specifically the cosine function, since we know the length of the ladder and the angle of inclination.

To calculate the horizontal distance, we use the formula: Horizontal Distance = Ladder Length × cosine(Inclination Angle). Here, the ladder length is given as 9.00 m and the inclination angle is 75.0°. Using a calculator with the angle in degrees, we find:

Horizontal Distance = 9.00 m × cos(75.0°) = 9.00 m × 0.2588 = 2.33 m (rounded to two decimal places).

The horizontal distance from the bottom of the ladder to the building when the ladder is inclined at an angle of 75.0° to the horizontal is approximately 2.33 meters.

Answer 2

The question describes a right triangle with hypotenuse as 9 and one of the angles as 75 degrees. We are looking for the length of the leg adjacent the given angle 75 degrees.

Recall that:

`cos(\theta)=\cfrac{adj}{hyp}\\ \\ \Rightarrow\cos75^o=\cfrac{x}{9}\\ \\ \Rightarrow x=9\cos75^o=9(0.2588)=2.3 ft.`