Finding an angle using inverse trigonometry | AP Precalculus

Choose an inverse ratio from the two known sides.

Identify opposite, adjacent and hypotenuse relative to the unknown angle.
Use , or to recover the angle.

Ratio	Sides
	Opposite and hypotenuse
	Adjacent and hypotenuse
	Opposite and adjacent

Example 1

Find to 1 decimal place.

Apply inverse sin to both sides. Use degree mode;

is the acute angle in this right triangle.

Evaluate in degree mode and keep the full calculator value.

Keep the full value until the final step.

To 1 decimal place.

Example 2

Find to 1 decimal place.

Apply inverse cos to both sides. Use degree mode;

is the acute angle in this right triangle.

Evaluate in degree mode and keep the full calculator value.

Keep the full value until the final step.

To 1 decimal place.

Example 3

Find to 1 decimal place.

Apply inverse tan to both sides. Use degree mode;

is the acute angle in this right triangle.

Evaluate in degree mode and keep the full calculator value.

Keep the full value until the final step.

To 1 decimal place.

Remember
Use degree mode and round only the final answer.

Your turn

Question 1

Find to 1 decimal place.

Check answer

Apply inverse sin to both sides. Use degree mode;

is the acute angle in this right triangle.

Evaluate in degree mode and keep the full calculator value.

Keep the full value until the final step.

To 1 decimal place.

Question 2

Find to 1 decimal place.

Check answer

Apply inverse cos to both sides. Use degree mode;

is the acute angle in this right triangle.

Evaluate in degree mode and keep the full calculator value.

Keep the full value until the final step.

To 1 decimal place.

Question 3

Find to 1 decimal place.

Check answer

Apply inverse tan to both sides. Use degree mode;

is the acute angle in this right triangle.

Evaluate in degree mode and keep the full calculator value.

Keep the full value until the final step.

To 1 decimal place.

Question 4

Find to 1 decimal place.

Check answer

Apply inverse sin to both sides. Use degree mode;

is the acute angle in this right triangle.

Evaluate in degree mode and keep the full calculator value.

Keep the full value until the final step.

To 1 decimal place.

Question 5

Find to 1 decimal place.

Check answer

Apply inverse cos to both sides. Use degree mode;

is the acute angle in this right triangle.

Evaluate in degree mode and keep the full calculator value.

Keep the full value until the final step.

To 1 decimal place.