도형의 성질 전체 문제

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

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

A 15-ft ladder leans against a building so that the angle between the ground and the ladder is $70^\circ .$ How high does the ladder reach up the side of the building? Find the answer to four decimal places.

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.

For the given right triangle, label the adjacent side, opposite side, and hypotenuse for the indicated angle.

When a right triangle with a hypotenuse of 1 is placed in the unit circle, which sides of the triangle correspond to the x- and y-coordinates?

The tangent of an angle compares which sides of the right triangle?

What is the relationship between the two acute angles in a right triangle?

Explain the cofunction identity.

For the following exercises, use cofunctions of complementary angles.

$\cos (34^\circ )=\sin (\_\_^\circ )$

For the following exercises, use cofunctions of complementary angles.

$\cos \left(\frac{\pi }{3}\right)=\sin (\_\_\_)$

For the following exercises, use cofunctions of complementary angles.

$\csc (21^\circ )=\sec (\_\_\_^\circ )$

For the following exercises, use cofunctions of complementary angles.

$\tan \left(\frac{\pi }{4}\right)=\cot (\_\_)$

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 (the referenced figure) to evaluate each trigonometric function of angle $A.$

$\sin \,A$