Trigonometry

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 one leg.

Front

How do you find the angle of elevation when given the height and distance from the base?

Back

Use the tangent function: tan(angle) = opposite/adjacent, where 'opposite' is the height and 'adjacent' is the distance from the base.

Front

What is the formula to calculate the height of an equilateral triangle?

Back

The height (h) of an equilateral triangle with side length (s) is given by h = (√3/2) * s.

Front

What is the cosine ratio in a right triangle?

Back

The cosine ratio is defined as the length of the adjacent side divided by the length of the hypotenuse: cos(angle) = adjacent/hypotenuse.

Front

What is the sine ratio in a right triangle?

Back

The sine ratio is defined as the length of the opposite side divided by the length of the hypotenuse: sin(angle) = opposite/hypotenuse.

Front

What is the tangent ratio in a right triangle?

Back

The tangent ratio is defined as the length of the opposite side divided by the length of the adjacent side: tan(angle) = opposite/adjacent.

Front

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

Back

Use the Pythagorean theorem: a² + b² = c², where 'c' is the hypotenuse and 'a' and 'b' are the other two sides.

Front

What is the approximate value of √3?

Back

The approximate value of √3 is 1.732.

Front

What is the significance of the 30-60-90 triangle in trigonometry?

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

How do you calculate the angle of a ramp using trigonometric ratios?

Back

Use the sine, cosine, or tangent ratios based on the known sides of the triangle formed by the ramp.