A 5 feet long ladder leans against a wall and makes an angle of 65 degrees with the ground. find, to the nearest tenth of a foot, the distance from the wall to the base of the ladder.
90/65=.7222*5=3.6111+5=8.6111
8.1 feet
To find the distance from the wall to the base of the ladder, you can use trigonometry. The ladder forms a right triangle with the wall and the ground. The length of the ladder is the hypotenuse of the triangle, and the distance from the wall to the base is one of the legs.
In this case, the hypotenuse (length of the ladder) is given as 5 feet, and the angle between the ground and the ladder is 65 degrees. We need to find the length of the leg (distance from the wall to the base).
Using the trigonometric function cosine (cos), we can solve for the leg. The cosine of an angle is equal to the adjacent side divided by the hypotenuse.
cos(65°) = adjacent side / hypotenuse
Let's substitute the values and solve for the leg:
cos(65°) = x / 5
To find x, multiply both sides of the equation by 5:
5 * cos(65°) = x
Using a calculator, find the cosine of 65 degrees:
cos(65°) ≈ 0.4226
Multiply the cosine by 5:
5 * 0.4226 ≈ 2.1131
Rounding to the nearest tenth of a foot, the distance from the wall to the base of the ladder is approximately 2.1 feet.
To find the distance from the wall to the base of the ladder, we can use the trigonometric function cosine.
Let's call the distance we want to find "x." So, we want to find the value of x.
In this situation, we know the length of the ladder (5 feet) and the angle it makes with the ground (65 degrees). The ladder is the hypotenuse of a right triangle, the ground represents the base, and the distance from the wall represents the height.
By using the cosine function, we can relate the angle to the ratio of the adjacent side to the hypotenuse.
The cosine of an angle is equal to the adjacent side divided by the hypotenuse. Therefore, we can write:
cos(65 degrees) = adjacent side / 5 feet
To find the adjacent side, rearrange the formula:
adjacent side = 5 feet * cos(65 degrees)
Now, let's calculate the value of the adjacent side:
adjacent side = 5 feet * cos(65 degrees) ≈ 5 feet * 0.423 = 2.115 feet
So, the distance from the wall to the base of the ladder is approximately 2.115 feet, rounded to the nearest tenth of a foot.