Trigonometry Applications

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 to an object above the horizontal level.

Front

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

Back

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

Front

What trigonometric function relates the opposite side and the adjacent side in a right triangle?

Back

The tangent function (tan).

Front

If the angle of elevation to the top of a tree is 48° and the distance from the tree is 50 feet, what is the height of the tree?

Back

Height = 50 * tan(48°) ≈ 46.5 feet.

Front

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

Back

Sine (sin) is the ratio of the length of the opposite side to the length of the hypotenuse.

Front

How do you calculate the height reached by a ladder leaning against a wall?

Back

Use the formula: height = length of ladder * sin(angle with the ground).

Front

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

Back

Cosine (cos) is the ratio of the length of the adjacent side to the length of the hypotenuse.

Front

If a ladder is 16 feet long and makes an angle of 68° with the ground, how high does it reach?

Back

Height = 16 * sin(68°) ≈ 14.8 feet.

Front

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

Back

The sides of a right triangle are related to the angles through trigonometric ratios: sin, cos, and tan.

Front

What is the formula for finding the distance from the base of a tree using the angle of elevation?

Back

Distance = height / tan(angle of elevation).