3. A ladder 14 ft long is leaning against a fence 8 ft high, with the upper end projecting over the fence. If the lower end slides away from the fence at the rate of 2 ft/sec, find the rate at which the angle between the ladder and the ground is changing when the upper end is just at the top of the fence.
Trigonometric Identities
Trigonometry in mathematics deals with the right-angled triangle’s angles and sides. By trigonometric identities, we mean the identities we use whenever we need to express the various trigonometric functions in terms of an equation.
Inverse Trigonometric Functions
Inverse trigonometric functions are the inverse of normal trigonometric functions. Alternatively denoted as cyclometric or arcus functions, these inverse trigonometric functions exist to counter the basic trigonometric functions, such as sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec). When trigonometric ratios are calculated, the angular values can be calculated with the help of the inverse trigonometric functions.
Solve the following problems using inverse trigonometric functions
![3. A ladder 14 ft long is leaning against a fence 8 ft high, with the upper end projecting over the fence. If the lower end slides away from the
fence at the rate of 2 ft/sec, find the rate at which the angle between the ladder and the ground is changing when the upper end is just at the top
of the fence.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F333c905d-21ca-405a-a104-2bf6605500f7%2F2bfb1fd6-8536-4bef-905e-36c8b6705b05%2Fda6mrij_processed.jpeg&w=3840&q=75)
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