Understanding Sine and Triangles

The video tutorial addresses a common trigonometric problem where sine theta equals 1.1, which is undefined. The teacher explains why this occurs, emphasizing the role of the hypotenuse in right triangles and the Pythagorean theorem. A practical demonstration helps visualize the relationship between angles and sides. The tutorial also covers solving trigonometric problems and introduces the ambiguous case of sine, highlighting potential pitfalls in calculations.

Why does a calculator return a math error when sine theta is greater than 1?

• Because sine cannot be calculated for angles greater than 90 degrees.

• Because sine values are always negative for angles greater than 90 degrees.

• Because the hypotenuse cannot be shorter than the opposite side.

• Because the calculator is not programmed to handle such values.

What is the sine function a ratio of in a right triangle?

• Opposite side to adjacent side

• Opposite side to hypotenuse

• Adjacent side to hypotenuse

• Hypotenuse to opposite side

Why is the hypotenuse always the longest side in a right triangle?

• Because it is opposite the smallest angle.

• Because it is opposite the right angle.

• Because it is the sum of the other two sides.

• Because it is always parallel to the base.

What happens to the side opposite an angle as the angle widens in a triangle?

• The opposite side lengthens.

• The opposite side remains the same.

• The opposite side becomes the hypotenuse.

• The opposite side shortens.

In a right triangle, which angle is always the largest?

• The obtuse angle

• The angle opposite the hypotenuse

• The acute angle

• The right angle

When solving for an angle using sine, what is the first step?

• Identify the opposite side and hypotenuse.

• Identify the adjacent side.

• Calculate the tangent of the angle.

• Use the cosine ratio.

What is the sine of an angle if the opposite side is 8 and the hypotenuse is 10?

• 0.8

• 0.6

• 1.25

• 0.75

What is the ambiguous case in trigonometry?

• When two angles are equal.

• When a triangle has no right angle.

• When there are two possible solutions for an angle.

• When the hypotenuse is unknown.

How can you resolve the ambiguity in a non-right-angled triangle?

• By using the tangent ratio.

• By measuring the sides again.

• By subtracting the angle from 180 degrees.

• By using the cosine rule.

Why is it important not to directly write the sine inverse as the answer?

• Because it is not applicable to right triangles.

• Because it is not a valid mathematical operation.

• Because it is always incorrect.

• Because it might not be the only solution.