삼각함수 전체 문제

For the following exercises, simplify the first trigonometric expression by writing the simplified form in terms of the second expression.

$\sec \,x;\,\sin \,x$

For the following exercises, simplify the first trigonometric expression by writing the simplified form in terms of the second expression.

$\cot \,x;\,\sin \,x$

For the following exercises, simplify the first trigonometric expression by writing the simplified form in terms of the second expression.

$\cot \,x;\,\csc \,x$

If a loading ramp is placed next to a truck, at a height of 4 feet, and the ramp is 15 feet long, what angle does the ramp make with the ground?

If a loading ramp is placed next to a truck, at a height of 2 feet, and the ramp is 20 feet long, what angle does the ramp make with the ground?

A woman is standing 8 meters away from a 10-meter tall building. At what angle is she looking to the top of the building?

Issa is standing 10 meters away from a 6-meter tall building. Travis is at the top of the building looking down at Issa. At what angle is Travis looking at Issa?

A 20-foot tall building has a shadow that is 55 feet long. What is the angle of elevation of the sun?

A 90-foot tall building has a shadow that is 2 feet long. What is the angle of elevation of the sun?

A spotlight on the ground 3 meters from a 2-meter tall man casts a 6 meter shadow on a wall 6 meters from the man. At what angle is the light?

A spotlight on the ground 3 feet from a 5-foot tall woman casts a 15-foot tall shadow on a wall 6 feet from the woman. At what angle is the light?

For the following exercises, find a solution to the following word problem algebraically. Then use a calculator to verify the result. Round the answer to the nearest tenth of a degree.

A person does a handstand with their feet touching a wall and their hands 1.5 feet away from the wall. If the person is 6 feet tall, what angle do their feet make with the wall?

For the following exercises, find a solution to the following word problem algebraically. Then use a calculator to verify the result. Round the answer to the nearest tenth of a degree.

A person does a handstand with her feet touching a wall and her hands 3 feet away from the wall. If the person is 5 feet tall, what angle do her feet make with the wall?

For the following exercises, find a solution to the following word problem algebraically. Then use a calculator to verify the result. Round the answer to the nearest tenth of a degree.

A 23-foot ladder is positioned next to a house. If the ladder slips at 7 feet from the house when there is not enough traction, what angle should the ladder make with the ground to avoid slipping?

For the following exercises, find the area of the triangle with the given measurements. Round each answer to the nearest tenth.

$a=5,c=6,\beta =\,35^\circ$

For the following exercises, find the area of the triangle with the given measurements. Round each answer to the nearest tenth.

$b=11,c=8,\alpha =28^\circ$

For the following exercises, find the area of the triangle with the given measurements. Round each answer to the nearest tenth.

$a=32,b=24,\gamma =75^\circ$

For the following exercises, find the area of the triangle with the given measurements. Round each answer to the nearest tenth.

$a=7.2,b=4.5,\gamma =43^\circ$

In order to estimate the height of a building, two students stand at a certain distance from the building at street level. From this point, they find the angle of elevation from the street to the top of the building to be 39°. They then move 300 feet closer to the building and find the angle of elevation to be 50°. Assuming that the street is level, estimate the height of the building to the nearest foot.

In order to estimate the height of a building, two students stand at a certain distance from the building at street level. From this point, they find the angle of elevation from the street to the top of the building to be 35°. They then move 250 feet closer to the building and find the angle of elevation to be 53°. Assuming that the street is level, estimate the height of the building to the nearest foot.