# A kite has 120 m of string attached to it when it flies at an elevation of 5 degrees. How far is...

## Question:

A kite has 120 m of string attached to it when it flies at an elevation of 5 degrees. How far is it above the hand holding it? Assume that the string is taut.

## The Trigonometric Ratios:

The trigonometric ratios connect the three sides of a right-angled triangle and its acute angles. The three basic trigonometric ratios are; sine (sin), cosine (cos) and tangent (tan).

If one of the acute angles in a right-angled triangle is {eq}\theta {/eq}, then the three trigoometric ratios of the angle {eq}\theta {/eq} are:

• {eq}\rm \sin \theta =\rm \dfrac{Opposite\; side}{Hypotenuse} {/eq}
• {eq}\rm \cos \theta =\rm \dfrac{Adjacent\; side}{Hypotenuse} {/eq}
• {eq}\rm \tan \theta =\rm \dfrac{Opposite\; side}{Adjacent\; side} {/eq}

Recall that the hypotenuse is the longest side of a right-angled triangle.

A kite makes a right-angled triangle with the length of the string as the hypotenuse side. If the length of the string is 120 m and the angle of elevation from the holder's hand is {eq}\theta = 5^\circ {/eq}, then the height of the kite from the hand holding it is equal to:

• {eq}\rm \sin 5 =\rm \dfrac{x}{120} {/eq}
• {eq}\rm x = \rm 120 \sin 5 \approx \boxed{10.46\, m} {/eq}