How do you calculate the sine of an angle given the opposite and hypotenuse?

To calculate the sine of an angle A, use the formula: $$\text{sin}(A) = \frac{\text{opposite}}{\text{hypotenuse}}$$ .

What is the sine ratio for angle A if the opposite side is 12 and the hypotenuse is 37?

The sine ratio for angle A is $$\frac{12}{37}$$ .

What is the relationship between sine and cosine in a right triangle?

In a right triangle, sine and cosine are related by the identity: $$\text{sin}(A) = \text{cos}(90^\text{o} - A)$$ .

What is the Pythagorean theorem?

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides: $$a^2 + b^2 = c^2$$ .

How do you find the length of a side in a right triangle using the Pythagorean theorem?

To find the length of a side, rearrange the Pythagorean theorem: $$c = \text{√}(a^2 + b^2)$$ .

What is the formula for the area of a triangle?

The area of a triangle can be calculated using the formula: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ .

What is the definition of a right triangle?

A right triangle is a triangle that has one angle measuring 90 degrees.

What is the significance of the hypotenuse in a right triangle?

The hypotenuse is the longest side of a right triangle, opposite the right angle.

IM2: Outcome 3 (All Components) Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

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

Back

The sine function (sin) of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the hypotenuse.

2.

FLASHCARD QUESTION

Front

What is the formula to find the unknown angle using sine?

Back

3.

FLASHCARD QUESTION

Front

What are the side ratios in a 30-60-90 triangle?

Back

4.

FLASHCARD QUESTION

Front

What is the length of the short leg in a 30-60-90 triangle if the hypotenuse is 6?

Back

5.

FLASHCARD QUESTION

Front

What is the length of the longer leg in a 30-60-90 triangle if the hypotenuse is 6?

Back

6.

FLASHCARD QUESTION

Front

What are the side ratios in a 45-45-90 triangle?

Back

7.

FLASHCARD QUESTION

Front

What is the length of the hypotenuse in a 45-45-90 triangle if each leg is 4?

Back

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