삼각비

For the following exercises, find the lengths of the missing sides if side $a$ is opposite angle $A,$ side $b$ is opposite angle $B,$ and side $c$ is the hypotenuse.

$\cos \,B=\frac{4}{5},a=10$

For the following exercises, find the lengths of the missing sides if side $a$ is opposite angle $A,$ side $b$ is opposite angle $B,$ and side $c$ is the hypotenuse.

$\sin \,B=\frac{1}{2},\,a=20$

For the following exercises, find the lengths of the missing sides if side $a$ is opposite angle $A,$ side $b$ is opposite angle $B,$ and side $c$ is the hypotenuse.

$\tan \,A=\frac{5}{12},b=6$

For the following exercises, find the lengths of the missing sides if side $a$ is opposite angle $A,$ side $b$ is opposite angle $B,$ and side $c$ is the hypotenuse.

$\tan \,A=100,b=100$

For the following exercises, find the lengths of the missing sides if side $a$ is opposite angle $A,$ side $b$ is opposite angle $B,$ and side $c$ is the hypotenuse.

$\sin \,B=\frac{1}{\sqrt{3}},\,a=2$

For the following exercises, find the lengths of the missing sides if side $a$ is opposite angle $A,$ side $b$ is opposite angle $B,$ and side $c$ is the hypotenuse.

$a=5,\,\measuredangle \,A={60}^{\circ }$

For the following exercises, find the lengths of the missing sides if side $a$ is opposite angle $A,$ side $b$ is opposite angle $B,$ and side $c$ is the hypotenuse.

$c=12,\,\measuredangle \,A={45}^{\circ }$

For the following exercises, use a calculator to find the length of each side to four decimal places.

$b=15,\,\measuredangle B={15}^{\circ }$

For the following exercises, use a calculator to find the length of each side to four decimal places.

$c=200,\,\measuredangle B={5}^{\circ }$

For the following exercises, use a calculator to find the length of each side to four decimal places.

$c=50,\,\measuredangle B={21}^{\circ }$

For the following exercises, use a calculator to find the length of each side to four decimal places.

$a=30,\,\measuredangle A={27}^{\circ }$

For the following exercises, use a calculator to find the length of each side to four decimal places.

$b=3.5,\,\measuredangle A={78}^{\circ }$

A 200-foot tall monument is located in the distance. From a window in a building, a person determines that the angle of elevation to the top of the monument is $15^\circ ,$ and that the angle of depression to the bottom of the tower is $2^\circ .$ How far is the person from the monument?

A 400-foot tall monument is located in the distance. From a window in a building, a person determines that the angle of elevation to the top of the monument is $18^\circ ,$ and that the angle of depression to the bottom of the monument is $3^\circ .$ How far is the person from the monument?

The angle of elevation to the top of a building in New York is found to be 9 degrees from the ground at a distance of 1 mile from the base of the building. Using this information, find the height of the building.

The angle of elevation to the top of a building in Seattle is found to be 2 degrees from the ground at a distance of 2 miles from the base of the building. Using this information, find the height of the building.

Assuming that a 370-foot tall giant redwood grows vertically, if I walk a certain distance from the tree and measure the angle of elevation to the top of the tree to be $60^\circ ,$ how far from the base of the tree am I?

For the following exercises, use side lengths to evaluate.

$\cos \,\frac{\pi }{4}$

For the following exercises, use side lengths to evaluate.

$\cot \,\frac{\pi }{3}$

For the following exercises, use side lengths to evaluate.

$\tan \,\frac{\pi }{6}$