A ladder leans up against a wall forming a 25 degree angle with the wall. If the ladder reaches 2.8 metres up the wall, how long is the ladder to the nearest metre?
We can use trigonometry to solve this problem. The length of the ladder is the hypotenuse of a right triangle, with the height of the ladder on the wall being the opposite side and the distance from the base of the ladder to the wall being the adjacent side.
Using the sine function, we can write:
sin(25 degrees) = opposite/hypotenuse
Rearranging the equation, we get:
hypotenuse = opposite / sin(25 degrees)
Plugging in the values, we have:
hypotenuse = 2.8 / sin(25 degrees)
Calculating sin(25 degrees), we find:
sin(25 degrees) ≈ 0.4226
Substituting this value into the equation, we have:
hypotenuse = 2.8 / 0.4226
hypotenuse ≈ 6.62
Therefore, the length of the ladder to the nearest meter is 7 meters.