Find a value of alpha  in the interval [0 degrees, 90 degrees] that satisfies the given statement: cot alpha  = 1.4895954.  ?

cot(α) = 1.4895954

tan(α) = 1/cot(α)
tan(α) = 1/1.4895954
α = tan⁻¹(1/1.4895954)

By using a calculator, α = 33.874380°

I'm replacing your alpha with x. Find x in (0,90) such that cotx = 1.4895954.;
For such x we have tanx = 1/cotx = 1/1.4895954 = 0.6713232331. Then x =;
arctan(0,6713232331) =  33.87437957 degrees. I hope your calculator has the
arctan function.