For safety reasons, the angle between a ladder and the ground should be between 65° and 80. A ladder that is 5 m long is placed so that it reaches a window on the top floor of a house. If the foot of the ladder is 1.5 m from the house, is the ladder safe? Explain your answer.
NO!!
the cos is adjacent/hypotenuse
which is distance along ground / length of ladder
to use tangent you need the height
h^2 = 5^2 - 1.5^2
tan (angle) = h/1.5
cos angle = 1.5/5
angle = 72.5 degrees
well that is between 65 and 80
if the same goes for tangent ratio can i do 5/1.5 to get 73 degrees as well?
i understand now thank you damon!!
You are welcome :)
To determine if the ladder is safe, we need to find the angle between the ladder and the ground. In this case, we have the length of the ladder (5m) and the distance between the foot of the ladder and the house (1.5m).
To find the angle, we can use the trigonometric function called arctan (also known as the inverse tangent). The formula to calculate the angle is:
angle = arctan(opposite/adjacent)
In this case, the opposite side is the height (h) of the ladder, and the adjacent side is the distance between the foot of the ladder and the house.
We can use the Pythagorean theorem to find the height of the ladder:
h^2 = 5^2 - 1.5^2
h^2 = 25 - 2.25
h^2 = 22.75
h ≈ √22.75
h ≈ 4.77m
Now, we can calculate the angle:
angle = arctan(4.77/1.5)
angle ≈ arctan(3.18)
angle ≈ 71.26°
The calculated angle is approximately 71.26°.
Based on the given safety guidelines, which state that the angle should be between 65° and 80°, the ladder is safe. The angle of 71.26° falls within this range.
Therefore, we can conclude that the ladder is safe to use.