Pythagorean Theorem and Right Triangle Trig Word Problems

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). It can be expressed as: c² = a² + b².

Front

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

Back

To find the length of the hypotenuse, use the Pythagorean Theorem: c = √(a² + b²), where c is the hypotenuse and a and b are the lengths of the other two sides.

Front

What is a right triangle?

Back

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

Front

If one leg of a right triangle is 6 feet and the other leg is 8 feet, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(6² + 8²) = √(36 + 64) = √100 = 10 feet.

Front

What is the definition of 'angle of elevation'?

Back

The angle of elevation is the angle formed by the horizontal line and the line of sight to an object above the horizontal line.

Front

How do you solve for the height of an object using the angle of elevation?

Back

Use the tangent function: height = distance * tan(angle of elevation).

Front

What is the tangent of an angle in a right triangle?

Back

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

Front

If a ladder is leaning against a wall and forms a right triangle, how can you find the distance from the base of the wall?

Back

Use the Pythagorean Theorem: distance = √(ladder length² - wall height²).

Front

What is the sine of an angle in a right triangle?

Back

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

Front

What is the cosine of an angle in a right triangle?

Back

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