도형의 성질 전체 문제

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 monument is $2^\circ .$ How far is the person from the monument?

The angle of elevation to the top of a building in Charlotte 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.

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

For the following exercises, use side lengths to evaluate.

$\cos \left(\frac{\pi }{2}\right)=\sin (\_\_\_^\circ )$

For the following exercises, use side lengths to evaluate.

$\csc (18^\circ )=\sec (\_\_\_^\circ )$

For the following exercises, use the given information to find the lengths of the other two sides of the right triangle.

$\cos \,B=\frac{3}{5},a=6$

For the following exercises, use the given information to find the lengths of the other two sides of the right triangle.

$\tan \,A=\frac{5}{9},b=6$

For the following exercises, solve for the unknown sides of the given triangle.

The angle of elevation to the top of a building in Baltimore is found to be 4 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. Find the answer to four decimal places.