A ladder, leaning against a wall, makes an angel 60¡ã with the horizontal. If the foot of the ladderis 2.5 m away from the wall, find the length of the ladder
Draw a diagram first
Then let the base be 2.5m i.e AB=2.5
Cos 60° =b/h = AB/AC
or,1/2=2.5/AC
2=AC/2.5
or, AC =5m
cn u help me
draw a diagram.
review your basic trig functions.
Now it is clear that
2.5/x = cos60°
now just solve for x, the length of the ladder.
To find the length of the ladder, we can use the trigonometric function sine, as it is defined as the ratio of the opposite side to the hypotenuse in a right triangle.
In this case, the ladder forms a right triangle with the wall and the ground. The angle between the ladder and the ground is given as 60 degrees (θ) and the distance from the foot of the ladder to the wall is given as 2.5 meters.
Let's label the length of the ladder as 'l' and the height of the ladder on the wall as 'h'.
Using the trigonometric function sine, we have:
sin θ = opposite/hypotenuse
sin 60° = h/l
We know that sin 60° is equal to (√3)/2, so we can substitute that in the equation:
(√3)/2 = h/l
To isolate 'l', we can cross multiply:
l = h / (√3)/2
Now, we need to find the value of 'h'. In the right triangle, we can use trigonometric function cosine, as it is defined as the ratio of the adjacent side to the hypotenuse.
cos θ = adjacent/hypotenuse
cos 60° = 2.5/l
We know that cos 60° is equal to 1/2, so we can substitute that in the equation:
1/2 = 2.5/l
To isolate 'l', we can cross multiply:
l = (2.5 * 2) / 1
Simplifying, we get:
l = 5 / 1
l = 5 meters
Therefore, the length of the ladder is 5 meters.