A ladder 36m long rests against a wall, its foot being at a horizontal distance of 25m from the base of the wall. What angle does the ladder make with the ground?

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Answer 1 · 2018-03-07T11:29:01

The ladder makes ${46.02}^{0}$ $46.02^0$ angle with the ground.

In the right triangle formed by the ladder, wall and ground, base is

$b = 25$ $b=25$ m , hypotenuse is $h = 36$ $h=36$ m. Let the angle formed by the

ladder with the ground is $theta :. cos theta= b/h=25/36$

$:. theta=cos^-1(25/36) or theta ~~ 46.02^0$

The ladder makes $46.02^0$ angle with the ground. [Ans]

Answer 2 · 2018-03-07T11:35:45

$0.803" radians"color(white)("xx")=color(white)("xx")46.0^circ$ (approx.)

enter image source here

By basic trig definitions (for the above diagram):
$color(white)("XXX")cos(theta)=25/36$
and
$color(white)("XXX")arccos(25/36)=theta$

That is
$color(white)("XXX")theta=arccos(25/36)=arccos(0.69bar4)=0.803" radians"$ (using a calculator to 3 decimal places)