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An aerial photograph from a U-2 spy plane is taken of a building suspected of housing nuclear warheads. The photograph is made when the angle of elevation of the sun is \(32^{\circ} .\) By comparing the shadow cast by the building to objects of known size in the photograph, analysts determine that the shadow is \(80 \mathrm{ft}\) long. How tall is the building (to the nearest foot)?

Find the degree measure of the smallest positive angle that is coterminal with each angle. $$ 900.54^{\circ} $$

True or false? Do not use a calculator. $$ \cos (6 \pi / 7)=-\cos (\pi / 7) $$

For each given angle name the quadrant in which the terminal side lies. $$ -7.3 $$

True or false? Do not use a calculator. $$ \cos (13 \pi / 12)=-\cos (\pi / 12) $$

Find the exact value of each expression without using a calculator. Check your answer with a calculator. $$ \frac{\sin (-5 \pi / 6)}{\cos (-5 \pi / 6)} $$

Achieving Synchronous Orbit The space shuttle orbits Earth in about 90 min at an altitude of about \(125 \mathrm{mi}\), but a communication satellite must always remain above a fixed location on Earth, in synchronous orbit with Earth. Since Earth rotates \(15^{\circ}\) per hour, the angular velocity of a communication satellite must be \(15^{\circ}\) per hour. To achieve a synchronous orbit with Earth, the radius of the orbit of a satellite must be 6.5 times the radius of Earth ( 3950 mi). What is the linear velocity in miles per hour of such a satellite?

Find the degree measure of the smallest positive angle that is coterminal with each angle. $$ 1235.6^{\circ} $$

True or false? Do not use a calculator. $$ \sin (23 \pi / 24)=-\sin (\pi / 24) $$

Find the exact value of each expression without using a calculator. Check your answer with a calculator. $$ \frac{\sin (7 \pi / 4)}{\cos (7 \pi / 4)} $$