A 1O-m ladder rests againts the wall of a house.The foot of the ladder on the ground is 1.3 m from the wall.What angle does the ladder make with the wall?

7.47

what is sin^-1 (1.3/10) ?

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

Tangent is defined as the ratio of the opposite side to the adjacent side in a right triangle. In this case, the opposite side is the height of the ladder and the adjacent side is the distance between the foot of the ladder and the wall.

Let's label the height of the ladder as 'h' and the distance between the foot of the ladder and the wall as 'd'.

We know that the ladder is 10 m long and the foot of the ladder is 1.3 m from the wall. So we have:

d = 1.3 m
ladder length = 10 m

Now we can use tangent to find the angle theta that the ladder makes with the wall:

tan(theta) = h / d

Substituting the values that we have:

tan(theta) = h / 1.3

To find theta, we can take the inverse tangent (arctan) of both sides:

theta = arctan(h / 1.3)

To find h, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (ladder length) is equal to the sum of the squares of the other two sides (height and distance from the wall).

Hence, h^2 + d^2 = ladder length^2

Substituting the values that we have:

h^2 + 1.3^2 = 10^2

h^2 + 1.69 = 100

h^2 = 98.31

h ≈ 9.915

Now we can substitute this value into the equation for theta:

theta = arctan(9.915 / 1.3)

Using a scientific calculator or an online calculator that has the arctan function, we can find the value of theta to be approximately 81.70 degrees.

Therefore, the ladder makes an angle of approximately 81.70 degrees with the wall.

To find the angle that the ladder makes with the wall, we can use trigonometric functions. In this case, we can use the tangent function.

Given that the foot of the ladder on the ground is 1.3 m from the wall and the length of the ladder is 10 m, we can form a right triangle with the wall, the ladder, and the distance from the foot of the ladder to the wall.

Let's call the angle that the ladder makes with the wall θ.

Using the tangent function, we have:

tan(θ) = opposite/adjacent

In this case, the opposite side is the height of the wall (10 m) and the adjacent side is the distance from the foot of the ladder to the wall (1.3 m).

So, we can write the equation as:

tan(θ) = 10/1.3

Now, to find θ, we can take the inverse tangent (arctan) of both sides of the equation.

θ = arctan(10/1.3)

Using a calculator or a trigonometric table, we can find the value of θ.