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Right triangles & trigonometry: FAQ

Frequently asked questions about right triangles & trigonometry

What are the trigonometric ratios?

The ratios of the sides of a right triangle are called trigonometric ratios. Three common trigonometric ratios are the sine (sin), cosine (cos), and tangent (tan). These are defined for acute angle A below:
In these definitions, the terms opposite, adjacent, and hypotenuse refer to the lengths of the sides.

Where are these topics used in the real world?

Trigonometry is used in a lot of different fields! Architects and engineers use trigonometry to design buildings and bridges. Surveyors use it to measure distances and angles. Astronomers use trigonometry to measure distances between stars and galaxies. In addition, carpenters, artists, and even athletes can use the principles of right triangle trigonometry in their work.

What do we know about the sine and cosine of complementary angles?

Knowing the sine and cosine of complementary angles can be helpful when solving problems with right triangles. The sine of an angle is equal to the cosine of its complementary angle, and vice versa. So if we know the cosine of an angle, we can use that information to find the sine of its complementary angle, or vice versa.

How do we use the reciprocal trigonometric ratios?

The reciprocal trigonometric ratios are just the inverses of the regular trigonometric ratios: cosecant is the reciprocal of sine, secant is the reciprocal of cosine, and cotangent is the reciprocal of tangent. We can use them in the same way we use the regular trigonometric ratios, to solve for side lengths or angles in right triangles.

What do we mean by modeling with right triangles?

We can use right triangles to model real-world situations. For example, we might use a right triangle to figure out the height of a building or the distance across a river. Modeling with right triangles can help us solve problems we wouldn't be able to solve otherwise.

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