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

The sides of a right triangle are related to the angles through trigonometric ratios, which allow us to calculate unknown side lengths when angles are known.

If the angle is 46 degrees and the opposite side is 17, how do you find the hypotenuse?

Use the sine ratio: $$\text{hypotenuse} = \frac{17}{\text{sine}(46)}$$ .

If the angle is 46 degrees and the hypotenuse is 20, how do you find the adjacent side?

Use the cosine ratio: $$\text{adjacent} = 20 \times \text{cosine}(46)$$ .

What is the formula to find the angle if two sides are known?

Use the inverse trigonometric functions: $$\theta = \text{sin}^{-1}igg(\frac{\text{opposite}}{\text{hypotenuse}}igg)$$ , $$\theta = \text{cos}^{-1}igg(\frac{\text{adjacent}}{\text{hypotenuse}}igg)$$ , or $$\theta = \text{tan}^{-1}igg(\frac{\text{opposite}}{\text{adjacent}}igg)$$ .

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 round a number to the nearest tenth?

To round a number to the nearest tenth, look at the hundredths place. If it is 5 or greater, round up; if it is less than 5, round down.

What is the significance of the angle in trigonometric ratios?

The angle determines the specific ratios of the sides in a right triangle, which are essential for solving problems involving right triangles.

How can you check if your answer for a missing side is correct?

You can check your answer by substituting the found side back into the trigonometric ratio and verifying if it holds true with the given angle.

Trig Ratios - Finding a Missing Side Flashcard

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the definition of a trigonometric ratio?

Back

A trigonometric ratio is a ratio of the lengths of two sides of a right triangle. The primary trigonometric ratios are sine, cosine, and tangent.

Tags

CCSS.HSG.SRT.C.6

2.

FLASHCARD QUESTION

Front

What is the sine ratio in a right triangle?

Back

Tags

CCSS.HSG.SRT.C.6

3.

FLASHCARD QUESTION

Front

What is the cosine ratio in a right triangle?

Back

Tags

CCSS.HSG.SRT.C.6

4.

FLASHCARD QUESTION

Front

What is the tangent ratio in a right triangle?

Back

Tags

CCSS.HSG.SRT.C.6

5.

FLASHCARD QUESTION

Front

How do you find a missing side using the sine ratio?

Back

Tags

CCSS.HSG.SRT.C.8

6.

FLASHCARD QUESTION

Front

How do you find a missing side using the cosine ratio?

Back

Tags

CCSS.HSG.SRT.C.8

7.

FLASHCARD QUESTION

Front

How do you find a missing side using the tangent ratio?

Back

Tags

CCSS.HSG.SRT.C.8

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