Question

Mary's kite is flying ablve the beach at the end of a 75-meter string. If the angle of elevation to the kite measures 68° and Mary is holding the kite 1.2 meters off the ground, then determine the height of Mary's kite flight.

Answer 1

Answer:

We found h

See figure. The sine trigonometric ratio of the angle 68° is:

sin(68°) = h / 75 multiplied by 75 we get

75xsin(68°) = (h / 75)x75

75xsin(68°) = h resolvemos

69.54 m = h

Then we add 1.2 m with 69.54 m to obtain the height H, i.e.

H= 1.2 +69.54  

H = 70.74 m is the answer.

Answer 2

To solve such problems we must know trigonometric functions.

Trigonometric functions

$\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}$

$\rm Cos \theta=\dfrac{Base}{Hypotenuse}$

$\rm Tan \theta=\dfrac{Perpendicular}{Base}$

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

The height of Mary's kite flight is 70.74 meters.

Given to us

• Mary's kite is flying above the beach at the end of a 75-meter string
• the angle of elevation to the kite measures 68°
• Mary is holding the kite 1.2 meters off the ground,

Solution

Assumption

Let the distance between Mary's kite and Mary be x.

In ΔABC

$\rm Sine(\theta) = \dfrac{Perpendicular}{Hypotenuse}$

Substituting the values in the Sine formula,

$\rm Sine(\angle A)= \dfrac{BC}{AC}$

$\rm Sine(68^o)= \dfrac{x}{75}\\\\ x = Sine(68^o) \times{75}\\\\ x = 69.54\ m$

Thus, the value of x is 69.54 m.

Height of Mary's kite flight

Height of Mary's kite flight = x + 1.2 meters

                                            = 69.54 + 1.2 meters

                                            = 70.74 meters

Hence, the height of Mary's kite flight is 70.74 meters.

Learn more about Trigonometric functions:

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