A ladder 10 ft in length reaches 9 ft up a wall against which it leans. Find the angle, to the nearest

degree, that the ladder makes with the wall.

To find the angle that the ladder makes with the wall, we can use the trigonometric function sine. The sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. In this case, the length of the side opposite the angle is 9 ft and the length of the hypotenuse is 10 ft.

So, we have sin(angle) = opposite/hypotenuse
sin(angle) = 9/10

To find the angle, we need to take the inverse sine (sin^-1) of both sides of the equation.

angle = sin^(-1)(9/10)

Using a calculator, we can find that the angle is approximately 63.4 degrees.

Therefore, to the nearest degree, the ladder makes an angle of 63 degrees with the wall.

To find the angle that the ladder makes with the wall, we can use the trigonometric function called tangent.

The tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

In this case, the side opposite the angle is the height of the wall (9 ft) and the side adjacent to the angle is the base of the ladder on the ground (10 ft).

So, we can use the formula for tangent:

tan(angle) = opposite/adjacent

Substituting the given values:

tan(angle) = 9/10

To find the angle itself, we need to take the inverse tangent (also known as arctangent or tan^(-1)) of both sides:

angle = atan(9/10)

Using a scientific calculator or an online calculator, we find:

angle ≈ 41.99 degrees

Therefore, to the nearest degree, the angle that the ladder makes with the wall is approximately 42 degrees.

cosØ = 9/10

Ø = appr 25.8°

isn't 9 the hypotenuse??