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Illustrate a mid-air refueling scenario that military aircraft often enact. Assume the elevation angle that the hose makes with the plane being fueled is \(\boldsymbol{\theta}=36^{\circ}\). Illustrate a mid-air refueling scenario that military aircraft often enact. Assume the elevation angle that the hose makes with the plane being fueled is \(\boldsymbol{\theta}=36^{\circ}\). (IMAGE CANNOT COPY) If the hose is 150 feet long, what should be the altitude difference \(a\) between the two planes? Round to the nearest foot.

Evaluate the following expressions exactly: $$\cot 150^{\circ}$$

In an oblique triangle \(A B C, \beta=45^{\circ}, \gamma=60^{\circ},\) and \(b=20\) in. Find the length of \(a\). Round your answer to the nearest unit.

In an oblique triangle \(A B C, b=30 \mathrm{cm}, c=45 \mathrm{cm},\) and \(\gamma=35^{\circ} .\) Find the length of \(a .\) Round your answer to the nearest unit.

Determine the angle of the smallest possible positive measure that is coterminal with each of the angles whose measure is given. Use degree or radian measures accordingly. $$-30$$

Let \(A, B,\) and \(C\) be the lengths of the three sides with \(X, Y,\) and \(Z\) as the corresponding angle measures in a triangle. Write a program using a TI calculator to solve each triangle with the given measures. $$B=24.5, C=31.6, \text { and } X=81.5^{\circ}$$

Find the smallest positive measure of \(\theta\) (rounded to the nearest degree) if the indicated information is true. \(\sin \theta=-0.3420\) and the terminal side of \(\theta\) lies in quadrant IV.

Let \(A, B,\) and \(C\) be the lengths of the three sides with \(X, Y,\) and \(Z\) as the corresponding angle measures in a triangle. Write a program using a TI calculator to solve each triangle with the given measures. $$A=29.8, B=37.6, \text { and } C=53.2$$

Find the exact length of the are made by the indicated central angle and radius of each circle. $$\theta=14^{\circ}, r=15 \mu \mathrm{m}$$

Determine whether each statement is true or false. If you are given the measures of two sides of a right triangle, you can solve the right triangle.