Tangent Ratio

Front

What is the tangent ratio in a right triangle?

Back

The tangent ratio is the ratio of the length of the opposite side to the length of the adjacent side. It is defined as tan(θ) = opposite/adjacent.

Front

How do you find the length of the shadow cast by an object when given the height and angle of elevation?

Back

Use the formula: shadow length = height / tan(angle of elevation).

Front

In a right triangle, if one angle is 40° and the opposite side is 25 ft, what is the length of the adjacent side?

Back

Use the formula: adjacent = opposite / tan(angle). So, adjacent = 25 / tan(40°) ≈ 25 / 0.8391 ≈ 29.8 ft.

Front

What does the term 'opposite side' refer to in a right triangle?

Back

The opposite side is the side opposite the angle of interest in a right triangle.

Front

What is the relationship between the tangent ratio and the angles in a right triangle?

Back

The tangent ratio relates the angles of a right triangle to the lengths of its sides, specifically the opposite and adjacent sides.

Front

If the height of a flagpole is 21 ft and it casts a shadow of 25 ft, what is the angle of elevation?

Back

Use the formula: angle = arctan(opposite/adjacent). So, angle = arctan(21/25) ≈ 40.2°.

Front

What is the formula to calculate the height of an object using the tangent ratio?

Back

Height = shadow length * tan(angle of elevation).

Front

In the context of tangent ratios, what does 'adjacent side' mean?

Back

The adjacent side is the side next to the angle of interest in a right triangle, excluding the hypotenuse.

Front

How can you estimate the height of a tree using a kite and the tangent ratio?

Back

Measure the distance from the kite to the base of the tree and the angle of elevation to the kite, then use height = distance * tan(angle).

Front

What is the tangent of a 45° angle?

Back

The tangent of a 45° angle is 1, meaning the opposite and adjacent sides are equal.