a ladder leans against a building forming an angle of 56 degrees with the ground.The base of the ladder is 3 feet from the building. Use the cosine to determine the length of the ladder.
Did you know that ladders are experts at reaching new heights? So, here's how we can calculate the length of your ladder using some clown-ish math humor:
First, we'll need to apply the Cosine function because it sounds more glamorous than "clownside." The Cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse in a right triangle.
In this case, the base of the ladder forms the adjacent side, and its length is given as 3 feet. The hypotenuse is represented by the length of the ladder, which we'll call "L."
Now, let's plug in the values into the cosine formula:
Cos(56 degrees) = 3 feet / L
To solve for L, we'll rearrange the equation:
L = 3 feet / Cos(56 degrees)
Now, let's consult our clown-calculator with its advanced laughter algorithms to find the answer:
L ≈ 6.13 feet
So, the length of your ladder is approximately 6.13 feet. Time to reach new heights, my friend!
To determine the length of the ladder, we can use the cosine function. The cosine function relates the adjacent side and the hypotenuse of a right triangle.
In this scenario, the base of the ladder (adjacent side) is the side of the right triangle that is 3 feet from the building, and the length of the ladder (hypotenuse) is what we want to find.
We know that the angle formed between the ladder and the ground is 56 degrees. Since the cosine of an angle is equal to the adjacent side divided by the hypotenuse, we can use this information to set up the equation:
cos(56°) = adjacent/hypotenuse
Now, let's substitute the values:
cos(56°) = 3/ladder length
To solve for the length of the ladder, we can rearrange the equation to isolate the ladder length on one side:
ladder length = 3/cos(56°)
Using a calculator, we can find the cosine of 56 degrees:
cos(56°) ≈ 0.559193
Now, we can substitute the value of cosine into the equation:
ladder length = 3/0.559193
Calculating this division, we find the length of the ladder:
ladder length ≈ 5.36 feet
Therefore, the length of the ladder is approximately 5.36 feet.
To find the length of the ladder, we can use the cosine function. The cosine of an angle in a right triangle is defined as the ratio of the adjacent side to the hypotenuse.
In this case, the angle formed between the ladder and the ground is given as 56 degrees. The base of the ladder, which is the side adjacent to the angle of 56 degrees, is 3 feet.
Let's use the cosine function to find the length of the ladder. The formula is:
cos(angle) = adjacent side / hypotenuse
Substituting the known values:
cos(56 degrees) = 3 feet / hypotenuse
Now, we solve for the length of the ladder (hypotenuse).
First, we need to find the cosine of 56 degrees. You can consult a trigonometric table or use a scientific calculator that has the cosine function. The cosine of 56 degrees is approximately 0.559.
Now we can substitute this value in the equation:
0.559 = 3 feet / hypotenuse
To solve for the hypotenuse, we rearrange the equation:
hypotenuse = 3 feet / 0.559
Using a calculator, we divide 3 feet by 0.559 to find the hypotenuse:
hypotenuse ≈ 5.368 feet
Therefore, the length of the ladder is approximately 5.368 feet.
They even told what to do with this right-angled triangle.
Did you make a sketch of the situation, then
cos 56° = 3/x , where x is the length of the ladder
x = 3/cos 56° = ...