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.

Tags

CCSS.HSG.SRT.C.6

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).

Tags

CCSS.HSG.SRT.C.8

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.

Tags

CCSS.HSG.SRT.C.8

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.

Tags

CCSS.HSG.SRT.C.6

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°.

Tags

CCSS.HSG.SRT.C.8

Front

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

Back

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

Tags

CCSS.HSG.SRT.C.8

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.

Tags

CCSS.HSG.SRT.C.6

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).

Tags

CCSS.HSG.SRT.C.8

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.

Tags

CCSS.HSG.SRT.C.6