Tom wants to clean his second story windows and plans to buy a ladder that will reach at least 20 feet high. If he leans the ladder against the house so that the base of the ladder makes a 59 degree angle with the ground, how long of a ladder should he buy? Round to a whole number as necessary. The ladder length is \( \square \) feet. (Round to a whole number as needed.)

Verify that the equation is an identity. \[ \cos ^{2} \theta\left(\tan ^{2} \theta+1\right)=1 \]

Realiza lo que se indica. Halla \( \alpha \) y \( \beta \) para que las relaciones sean válidus \( \tan \left(3 \alpha+15^{\circ}\right)=\cot \left(\beta+6^{\circ}\right) \) y \( \sec \left(\alpha+54^{\circ}\right)=\cos \left(2 \beta-12^{\circ}\right) \) \( \tan (3 \alpha+15)=\cot (\beta+6)(\sec (\alpha+54)=\cos (2 \beta-12) \)

A. \( \arccos \left(-\frac{\sqrt{2}}{2}\right)=x \)

Solve the equation \( 5 \sin 2 x+2=0 \) for \( 0^{\circ} \leq x \leq 360^{\circ} \) Correct your answer to 1 decimal place.

C. \( \arcsin \frac{\sqrt{2}}{2}=x \)