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

The tangent of an angle (A) is defined as the ratio of the length of the opposite side to the length of the adjacent side: $$\text{tan}(A) = \frac{\text{Opposite}}{\text{Adjacent}}$$ .

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

The relationship can be expressed as: $$\text{tan}(A) = \frac{\text{sin}(A)}{\text{cos}(A)}$$ .

How do you apply the Pythagorean Theorem to find the length of a side?

To find the length of a side, use the formula: if you know two sides, say a and b, then the hypotenuse c can be found using $$c = \text{sqrt}(a^2 + b^2)$$ .

What is the formula for finding the hypotenuse in a right triangle?

The formula for finding the hypotenuse (c) in a right triangle is: $$c = \text{sqrt}(a^2 + b^2)$$ .

What is the formula for finding a leg in a right triangle?

To find a leg (a) in a right triangle when the hypotenuse (c) and the other leg (b) are known, use: $$a = \text{sqrt}(c^2 - b^2)$$ .

What is the significance of the Pythagorean Theorem in real life?

The Pythagorean Theorem is used in various fields such as architecture, construction, navigation, and physics to calculate distances and ensure structures are built correctly.

How can you verify if a triangle is a right triangle using the Pythagorean Theorem?

To verify if a triangle is a right triangle, check if the squares of the lengths of the two shorter sides add up to the square of the length of the longest side: $$a^2 + b^2 = c^2$$ .

What is the relationship between the angles and sides in a right triangle?

In a right triangle, the angles are related to the sides through trigonometric ratios, and the sum of the angles is always 180°, with one angle being 90°.

Pythagorean Theorem and Trig Review Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is the Pythagorean Theorem?

Back

Tags

CCSS.8.G.B.8

2.

FLASHCARD QUESTION

Front

How do you solve for x in a right triangle using the Pythagorean Theorem?

Back

Tags

CCSS.8.G.B.7

3.

FLASHCARD QUESTION

Front

What are the three main trigonometric ratios?

Back

The three main trigonometric ratios are: 1. Sine (sin) = Opposite/Hypotenuse 2. Cosine (cos) = Adjacent/Hypotenuse 3. Tangent (tan) = Opposite/Adjacent.

Tags

CCSS.HSG.SRT.C.6

4.

FLASHCARD QUESTION

Front

What is SOH CAH TOA?

Back

SOH CAH TOA is a mnemonic to remember the definitions of the sine, cosine, and tangent functions: SOH = Sine = Opposite/Hypotenuse, CAH = Cosine = Adjacent/Hypotenuse, TOA = Tangent = Opposite/Adjacent.

Tags

CCSS.HSG.SRT.C.6

5.

FLASHCARD QUESTION

Front

How do you find the missing angle in a right triangle using inverse trigonometric functions?

Back

Tags

CCSS.HSG.SRT.C.8

6.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.HSG.SRT.C.6

7.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.HSG.SRT.C.6

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