M13 Review Flashcard

Front

What is the height of an equilateral triangle in relation to its side length?

Back

The height (h) of an equilateral triangle can be calculated using the formula: h = (sqrt(3)/2) * side length.

Front

How do you find the length of each side of an equilateral triangle given its height?

Back

To find the side length (s) from the height (h), use the formula: s = (2/√3) * h.

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

In a right triangle, how do you determine the height of a ladder leaning against a wall?

Back

Use the Pythagorean theorem: if the ladder length is the hypotenuse and the distance from the wall is one leg, the height can be found using: height = √(ladder² - distance²).

Front

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

Back

The tangent of an angle in a right triangle is 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 and sides in a 30-60-90 triangle?

Back

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

Front

What is the relationship between the angles and sides in a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the length of the hypotenuse is √2 times the length of each leg.

Front

How do you solve for a variable using trigonometric functions?

Back

To solve for a variable using trigonometric functions, set up the appropriate ratio based on the angle and the sides involved, then isolate the variable.

Front

What is the formula for the height of a 30-60-90 triangle?

Back

The height (h) can be calculated as h = (√3/2) * hypotenuse.

Front

What is the formula for the height of a 45-45-90 triangle?

Back

The height (h) is equal to the length of one leg multiplied by √2: h = leg * √2.