Solving Right Triangles using Trigonometry

Front

What is a right triangle?

Back

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

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): c² = a² + b².

Front

What are the three main trigonometric ratios?

Back

The three main trigonometric ratios are sine (sin), cosine (cos), and tangent (tan). They are defined as follows: sin(θ) = opposite/hypotenuse, cos(θ) = adjacent/hypotenuse, tan(θ) = opposite/adjacent.

Front

How do you find the sine of an angle in a right triangle?

Back

To find the sine of an angle θ in a right triangle, divide the length of the side opposite the angle by the length of the hypotenuse: sin(θ) = opposite/hypotenuse.

Front

How do you find the cosine of an angle in a right triangle?

Back

To find the cosine of an angle θ in a right triangle, divide the length of the side adjacent to the angle by the length of the hypotenuse: cos(θ) = adjacent/hypotenuse.

Front

How do you find the tangent of an angle in a right triangle?

Back

To find the tangent of an angle θ in a right triangle, divide the length of the side opposite the angle by the length of the side adjacent to the angle: tan(θ) = opposite/adjacent.

Front

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

Back

In a right triangle, the sum of the angles is always 180 degrees, and one angle is always 90 degrees. The lengths of the sides are related through trigonometric ratios.

Front

What is the purpose of using trigonometry in solving right triangles?

Back

Trigonometry is used to find unknown side lengths and angle measures in right triangles using known values.

Front

How can you use the inverse trigonometric functions?

Back

Inverse trigonometric functions (sin⁻¹, cos⁻¹, tan⁻¹) are used to find angle measures when the lengths of the sides are known.

Front

What is the formula for finding the area of a right triangle?

Back

The area of a right triangle can be found using the formula: Area = (1/2) * base * height.