Trig word problems/ Pythagorean Identity

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

Define 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 calculate the height of an object using the angle of elevation?

Back

Height can be calculated using the formula: height = distance * tan(angle of elevation).

Front

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

Back

In a right triangle, the sine of an angle 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

In a right triangle, the cosine of an angle 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

In a right triangle, the tangent of an angle 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 find the distance from an object using the angle of elevation and height?

Back

Distance can be found using the formula: distance = height / tan(angle of elevation).

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, where 1 is the length of the side opposite the 30-degree angle.

Front

What is the relationship between the sides of 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 determine the height of a lighthouse using the angle of elevation?

Back

Use the formula: height = distance from the base * tan(angle of elevation).