a ladder which is 5 m long leans against a nail on the wall.it makes an angle of 62 derees with the ground. find the height of the nail above the ground and the distance of the foot of the ladder from the wall.
sin 62 = h/5
cos 62 = d/5
A ladder 6.4 meters long leans agant the wall of an apartment house forming an angle of 53%20% with the ground. How high up the wall does it reach?
h=4.41m
d=2.35m
A ladder that is 5m long leans against a nail on the wall. It makes an angle of 62⁰ with the ground.
To find the height of the nail above the ground and the distance of the foot of the ladder from the wall, we can use trigonometric functions.
Let's denote the height of the nail above the ground as h and the distance of the foot of the ladder from the wall as d.
We have a right triangle formed by the ladder, the ground, and the line connecting the nail to the foot of the ladder. The angle between the ladder and the ground is given as 62 degrees.
Using trigonometric functions, we can use the following equations:
sin(θ) = opposite/hypotenuse
cos(θ) = adjacent/hypotenuse
tan(θ) = opposite/adjacent
In this case, sin(62) = h/5 (opposite/hypotenuse)
Therefore, h = 5 * sin(62)
cos(62) = d/5 (adjacent/hypotenuse)
Therefore, d = 5 * cos(62)
Now, we can calculate these values:
h = 5 * sin(62) ≈ 4.55 meters (rounded to two decimal places)
d = 5 * cos(62) ≈ 2.69 meters (rounded to two decimal places)
So, the height of the nail above the ground is approximately 4.55 meters, and the distance of the foot of the ladder from the wall is approximately 2.69 meters.