Solving Right Triangles

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

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

Back

Sine of an angle (θ) is defined as the ratio of the length of the opposite side to the length of the hypotenuse: sin(θ) = opposite/hypotenuse.

Front

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

Back

Cosine of an angle (θ) is defined as the ratio of the length of the adjacent side to the length of the hypotenuse: cos(θ) = adjacent/hypotenuse.

Front

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

Back

Tangent of an angle (θ) is defined as the ratio of the length of the opposite side to the length of the adjacent side: tan(θ) = opposite/adjacent.

Front

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

Back

The sum of the angles in any triangle is 180 degrees. In a right triangle, the two non-right angles must add up to 90 degrees.

Front

How do you solve for a missing side in a right triangle using trigonometric ratios?

Back

You can use the sine, cosine, or tangent ratios depending on the known angles and sides. For example, if you know an angle and the hypotenuse, use sine or cosine to find the opposite or adjacent side.

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.

Front

How do you use the inverse trigonometric functions?

Back

Inverse trigonometric functions (sin⁻¹, cos⁻¹, tan⁻¹) are used to find angles when the sides of a triangle are known.

Front

What is the significance of the 30-60-90 triangle?

Back

In a 30-60-90 triangle, the sides are in a specific ratio: the lengths of the sides opposite the 30°, 60°, and 90° angles are in the ratio 1:√3:2.