Trigonometric Word Problems

Front

What is the definition of the angle of elevation?

Back

The angle of elevation is the angle formed by the horizontal line and the line of sight from an observer to an object above the horizontal line.

Front

In a right triangle, what is the relationship between the angles and the sides?

Back

In a right triangle, the side opposite an acute angle can be found using the sine function, while the adjacent side can be found using the cosine function.

Front

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

Back

The sine function is defined as the ratio of the length of the opposite side to the length of the hypotenuse.

Front

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

Back

The cosine function is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.

Front

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

Back

The tangent function is defined as the ratio of the length of the opposite side to the length of the adjacent side.

Front

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

Back

Height = Distance from the object * tan(angle of elevation).

Front

If a ladder makes a 60-degree angle with the ground and is 10 meters long, how high does it reach?

Back

Height = 10 * sin(60 degrees) = 5 * sqrt(3) meters.

Front

What is the formula to find the opposite side in a right triangle when the hypotenuse and angle are known?

Back

Opposite side = Hypotenuse * sin(angle).

Front

How do you find the height of a kite using the angle of elevation?

Back

Height = Length of string * sin(angle of elevation).

Front

What is the height of a tree if a person stands 20 meters away and looks up at a 30-degree angle?

Back

Height of tree = 20 * tan(30 degrees) + person's height.