3.TRIG 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: a² + b² = c².

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

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2. The side opposite the 30° angle is the shortest, the side opposite the 60° angle is √3 times the shortest side, and the hypotenuse is twice the shortest side.

Front

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

Back

The sine function (sin) of an angle in a right triangle is the ratio of the length of the opposite side to the length of the hypotenuse. It can be expressed as: sin(θ) = opposite/hypotenuse.

Front

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

Back

The cosine function (cos) of an angle in a right triangle is the ratio of the length of the adjacent side to the length of the hypotenuse. It can be expressed as: cos(θ) = adjacent/hypotenuse.

Front

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

Back

The tangent function (tan) of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side. It can be expressed as: tan(θ) = opposite/adjacent.

Front

How do you calculate the height of an object using angles of elevation?

Back

To calculate the height of an object using angles of elevation, use the formula: height = distance * tan(angle), where distance is the horizontal distance from the observer to the object.

Front

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

Back

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

Front

How do you find the distance from the base of a building when given the height and length of a cable?

Back

Use the Pythagorean Theorem: distance = √(cable length² - height²), where cable length is the hypotenuse and height is one of the other sides.