64°
Step-by-step explanation:
The 36-ft distance can be regarded as the opposite side of the triangle formed by the leaning ladder while its length of 40 ft is the hypotenuse. So using the definition of a sine of an angle, we know that
[tex]\sin \theta = \dfrac{opposite}{hypotenuse} = \dfrac{36\:\text{ft}}{40\:\text{ft}}[/tex]
or
[tex]\theta = \sin^{-1}\left(\dfrac{36}{40}\right) = \sin^{-1}(0.9)[/tex]
[tex]\:\:\:\:=64°[/tex]
