Real-Life Trigonometry: Calculate Heights and Angles

Front

What is the sine function in trigonometry?

Back

The sine function (sin) is a ratio of the length of the opposite side to the length of the hypotenuse in a right triangle.

Front

What is the cosine function in trigonometry?

Back

The cosine function (cos) is a ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle.

Front

What is the tangent function in trigonometry?

Back

The tangent function (tan) is a ratio of the length of the opposite side to the length of the adjacent side in a right triangle.

Front

How do you calculate the height of an object using trigonometry?

Back

Height can be calculated using the formula: height = distance * sin(angle) for vertical height.

Front

What is the 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.

Front

What is the angle of depression?

Back

The angle of depression is the angle formed by the horizontal line and the line of sight to an object below the horizontal.

Front

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

Back

Use the formula: angle = arctan(height/distance).

Front

What is the relationship between the sides of a right triangle and its angles?

Back

In a right triangle, the side lengths are proportional to the sine, cosine, and tangent of the angles.

Front

If a cyclist travels 200 meters up a 15-degree incline, how do you find the vertical distance gained?

Back

Use the formula: vertical distance = 200 * sin(15 degrees) = 51.76 meters.

Front

How do you calculate the height of a kite using the length of the string and the angle?

Back

Height = string length * sin(angle). For a 70-degree angle and 100 meters string, height = 100 * sin(70 degrees) = 93.97 meters.