Example relating trig function to side ratios | Basic trigonometry | Trigonometry | Khan Academy

TL;DR

Sort expressions into categories based on their values in relation to a given triangle's angles.

Transcript

Sort the expressions according to their values. You can put any number of cards in a category or leave a category empty. And so we have this diagram right over here, then we have these cards that have these expressions. And we're supposed to sort these into different buckets. So we're trying to say, well what is the length of segment AC over the le... Read More

Key Insights

• 🙃 Ratios of lengths of sides in a right triangle can be matched to trigonometric functions.
• 🙃 Identifying the mentioned angles and sides is crucial in determining which trigonometric function applies to each expression.
• 🙃 The sine, cosine, and tangent functions are commonly used to express ratios of sides in a right triangle.

Questions & Answers

Q: Why is the length of segment AC over the length of segment BC equivalent to the sine of one of the angles in the triangle?

In a right triangle, the ratio of two sides is equal to the sine of one of its angles. In this case, segment AC is the side opposite to the angle in question, and segment BC is the hypotenuse.

Q: How do we determine the cosine of angle DEC when one of the sides mentioned is not adjacent to the angle?

The side mentioned in the expression is not adjacent to angle DEC. However, by considering another angle in the triangle, the ratio of the mentioned sides can be expressed as the sine of that angle instead.

Q: Why is the sine of angle CDA equal to the cosine of angle DAC?

The sine of angle CDA is actually equal to the cosine of angle DAC. This is because, relative to angle DAC, the ratio of the sides mentioned becomes the cosine function, as it deals with adjacent over hypotenuse.

Q: What trigonometric function applies to the ratio of the lengths of segments AE and EB?

The ratio of AE over EB corresponds to the sine of the angle included between the segments. In this case, it is equal to the sine of 41 degrees.

Summary & Key Takeaways

• The task is to sort expressions into categories based on their value in relation to the lengths of two sides of a right triangle.

• The expressions are ratios of lengths of sides in a right triangle, and they need to be matched to the appropriate trigonometric function.

• The key is to identify the angles and sides mentioned in the expressions and determine which trigonometric function applies to each one.