A30 ft ladder is leaning against a building. the ladder reaches the bottom of a window that is located 15 ft above the ground. what angle does the ladder make with the ground?

30 Degrees

Step-by-step explanation:

30 degrees  

Explanation:

This is clearly a right angle triangle question. In order to solve this question, one needs to understand the basics of a right angle triangle also called as "Right Triangle".  

What is Right Angle Triangle?

Simply, as the name suggests, right angle triangle is a triangle with one angle being the right angle (i.e 90 degrees) as shown in the schematics below.  

Furthermore, it consists of two legs making an angle of 90 degrees and a hypotenuse which is always the longest among other legs.

So, according to the question: Length of the ladder is 30 ft which is inclined on the building at a certain angle. In addition, it is given that the ladder touches the bottom of the window and window is located 15 ft above the ground.  

Step 1: First draw a schematic of this question which I have drawn and it is attached as schematic 2 in the attachment.  

Step 2: After carefully observing the schematic 2, we know that we have values of perpendicular and length of the ladder which is hypotenuse.  

Step 3: Applying a appropriate trigonometric function to calculate the angle. So, for right angle triangle, we have cosine function, Sine Function and Tangent Function.  

Sine(angle)  = Perpendicular / Hypotenuse

Cosine(angle) = Base / Hypotenuse

Tangent(angle) =  Perpendicular / Base

Step 4: So, according to the information given in the question which can be seen in the schematic 2, we have the values of perpendicular and hypotenuse. So, to calculate the angle between and ladder and the ground we need to use the first function which is the Sine function:  

                Sine (angle) = Perpendicular/ Hypotenuse

  Step 5: To calculate angle, equation will become:

               Angle = Sin-1 (Perpendicular/Hypotenuse)

              Angle = Sin-1 (15 ft/30 ft)  (Note: Put Sin inverse of 15/30 in calculator, you will get the angle)

              Angle = 30 Degrees    Answer.

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step-by-step explanation: