Trigonometry in Right-Angled Triangles

Define a right-angled triangle and its properties.

• A right-angled triangle has one angle of 90 degrees, with properties including the Pythagorean theorem and the relationship between its sides and angles.

• A right-angled triangle cannot be used in trigonometry.

• A right-angled triangle has all angles equal to 60 degrees.

• A right-angled triangle has two sides of equal length only.

What is the Pythagorean theorem? Provide the formula.

• c² = a × b

• a² + b² = c²

• a² - b² = c²

• a + b = c

If one leg of a right triangle is 6 cm and the other is 8 cm, find the hypotenuse.

• 10 cm

• 8 cm

• 14 cm

• 12 cm

Calculate the sine of an angle if the opposite side is 5 cm and the hypotenuse is 13 cm.

• 0.3846

• 0.5

• 0.7692

• 0.1538

Using SOH CAH TOA, what does SOH stand for?

• Sine = Opposite / Hypotenuse

• Sine = Adjacent / Hypotenuse

• Sine = Opposite / Adjacent

• Sine = Hypotenuse / Adjacent

If the adjacent side is 4 cm and the hypotenuse is 5 cm, find the cosine of the angle.

• 1.0

• 0.8

• 0.5

• 0.6

What is the tangent of an angle in a right triangle?

• The tangent of an angle is the ratio of the opposite side to the adjacent side.

• The tangent of an angle is the difference between the adjacent side and the hypotenuse.

• The tangent of an angle is the product of the opposite side and the hypotenuse.

• The tangent of an angle is the sum of the opposite and adjacent sides.

If the opposite side is 7 cm and the adjacent side is 24 cm, find the tangent of the angle.

• 1.2

• 0.5

• 0.75

• 0.2916666666666667

How do you find the angle using the inverse tangent function?

• Use the formula: angle = tan⁻¹(opposite/adjacent).

• angle = sin⁻¹(opposite/hypotenuse)

• angle = cos⁻¹(adjacent/hypotenuse)

• angle = tan(opposite + adjacent)

What is the relationship between sine, cosine, and tangent?

• Sine and cosine are the same function.

• Sine and cosine are unrelated to triangles.

• Tangent is the only function that relates to sine and cosine.

• Sine, cosine, and tangent are related through the ratios of the sides of a right triangle.