A ladder is leaning against the side of a house. The base of the ladder is 8 feet from the wall and makes an angle of 42 degree with the ground. Find the length of the ladder
no, like your namesake you are wrong
you want the hypotenuse , so
cos42 = 8/x
x = 8/cos42
= appr 10.77 ft
A ladder is leaning against the side of a house. The base of the ladder is 8 feet away from the wall, and the top of the ladder reaches a point on the house that is 15 feet above the ground. The ladder is x feet long. What is the value of x?
To find the length of the ladder, we can use the trigonometric function of sine or cosine, since we know the angle and one side of the right triangle formed by the ladder and the ground.
Let's denote the length of the ladder as "L".
The side opposite the angle of 42 degrees is the height of the ladder against the wall, which we can call "h". The side adjacent to the angle of 42 degrees is the distance from the base of the ladder to the wall, which is given as 8 feet.
Using the sine function:
sin(42 degrees) = h / L
Rearranging the formula, we have:
h = L * sin(42 degrees)
To solve for L, we need to find the value of h. We can do this by substituting the given side lengths and angle measure into the formula.
h = 8 feet * sin(42 degrees)
Using a calculator, find the sine of 42 degrees, and then multiply it by 8 feet to find h.
Once you have the value of h, you can substitute it back into the original formula and solve for L:
h = L * sin(42 degrees)
L = h / sin(42 degrees)
Now, use the calculated value of h and the trigonometric function sine to find the length of the ladder L.
tan(42)=x/8
x=7.2