The base 𝑥 of the right triangle in the figure increases at a rate of 5 cm/s, while the height remains constant at ℎ=17 cm.

Question

A diagram shows a right triangle. Height of the triangle measures h units and base measures x units. The angle between the base and the hypotenuse equals theta.

How fast is the angle 𝜃 changing when 𝑥=26?
(Use symbolic notation and fractions where needed.)

𝑑𝜃𝑑𝑡||||𝑥=26=

Answer 1

tanθ = 17/x
sec^2θ dθ/dt = -17/x^2 dx/dt
now plug and chug