Finding Missing Sides and Angles in Right Triangles

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). Formula: a² + b² = c².

Front

How do you find the length of a missing side in a right triangle?

Back

To find a missing side, use the Pythagorean Theorem. Rearrange the formula to solve for the missing side: a = √(c² - b²) or b = √(c² - a²).

Front

What is the sine function in relation to a right triangle?

Back

The sine function (sin) is the ratio of the length of the opposite side to the length of the hypotenuse. Formula: sin(θ) = opposite/hypotenuse.

Front

What is the cosine function in relation to a right triangle?

Back

The cosine function (cos) is the ratio of the length of the adjacent side to the length of the hypotenuse. Formula: cos(θ) = adjacent/hypotenuse.

Front

What is the tangent function in relation to a right triangle?

Back

The tangent function (tan) is the ratio of the length of the opposite side to the length of the adjacent side. Formula: tan(θ) = opposite/adjacent.

Front

How do you calculate the angle in a right triangle using trigonometric functions?

Back

To find an angle, use the inverse trigonometric functions: θ = sin⁻¹(opposite/hypotenuse), θ = cos⁻¹(adjacent/hypotenuse), or θ = tan⁻¹(opposite/adjacent).

Front

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

Back

In a right triangle, the sum of the three angles is always 180 degrees. One angle is 90 degrees, so the other two angles must sum to 90 degrees.

Front

If one angle in a right triangle is 30 degrees, what are the other two angles?

Back

If one angle is 30 degrees, the other two angles must be 90 degrees and 60 degrees, since 30 + 60 + 90 = 180.

Front

What is the formula to find the area of a right triangle?

Back

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

Front

How do you round a number to the nearest tenth?

Back

To round a number to the nearest tenth, look at the hundredths place. If it is 5 or greater, round up the tenths place by one. If it is less than 5, keep the tenths place the same.