A ladder 20m long rest against a vertical wall so that the foot of the ladder is 9m long. Find correct to the nearest degree the angle that the ladder makes with the wall.
Let the unknown number be x
Sin = opp
adj
Sinx°=9/20
Sinx°=0.45
Divide both sides by sin
Sinx°=0.45
Sin Sin
x°=0.45
Sin
x=sin raise to power -1,0.45
x=26.7
x=27° to the nearest degree.
sinB = 9/20 = 0.45.
B = 27o.
Nice and it remain the drawing
Let the unknown number be x
Tan x⁰= 9/20
Tan x⁰ =0•45
Divide both sides by tan
Tan x°/tan=0•45/tan
x°=tan raise to power-¹0•45
x=26•7
x=27°
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To the nearest degree, the angle the ladder makes with the wall is 27°.
To find the angle that the ladder makes with the wall, we can use the trigonometric function called the inverse tangent or atan.
The definition of the tangent function for a right triangle is 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 ladder is the hypotenuse, the side opposite is the height of the wall, and the side adjacent is the distance from the base of the ladder to the wall. We are given the lengths of these sides as follows:
Opposite side (height of the wall) = 20m
Adjacent side (distance from the base of the ladder to the wall) = 9m
Now, we can plug these values into the inverse tangent function to find the angle. We use the formula:
angle = atan(opposite side/adjacent side)
angle = atan(20/9)
Using a calculator, we can find that angle ≈ 64.4 degrees.
Therefore, the angle that the ladder makes with the wall is approximately 64.4 degrees.