a ladder is placed against the side of a building at an angle of 50 degree. the ladder's base is 10ft away from the base of the building. How long is the ladder?

10/(cos(50))=length of ladder

Trigonometry

To find the length of the ladder, we can use trigonometric functions, specifically the sine function.

Let's denote the length of the ladder as 'l'.

In this scenario, we have a right triangle formed by the ladder, the side of the building, and the ground. The angle between the ladder and the ground is given as 50 degrees.

We know that the sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse (the longest side of the triangle).

Therefore, we can write the equation as:

sin(50 degrees) = opposite side (length of the ladder) / hypotenuse (unknown)

We are given the value of the opposite side as 10 feet. So, we can rearrange the equation as:

l / 10 = sin(50 degrees)

To find the length of the ladder, we multiply both sides of the equation by 10:

l = 10 * sin(50 degrees)

Calculating the value of sin(50 degrees) and then multiplying it by 10 will give us the length of the ladder.