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An airplane is observed to be approaching the air point. It is at a distance of 12 km from the point of observation and makes an

angle of elevation of 50 degree. Find the height above the ground.

Respuesta :

MrRoyal

Answer:

The height is 14.3 km

Step-by-step explanation:

Given

[tex]distance= 12km[/tex]

[tex]\theta= 50[/tex] --- angle of elevation

Required

Determine the height above the ground

The question is illustrated using the attached image.

To calculate the required height, we make use of:

[tex]tan(\theta) = \frac{AB}{BC}[/tex]

Where AB represents the height and BC, the distance.

So:

[tex]tan(50) = \frac{AB}{12}[/tex]

Make AB the subject

[tex]AB = 12 * tan(50)[/tex]

[tex]AB = 12 * 1.1918[/tex]

[tex]AB = 14.3016[/tex]

[tex]AB = 14.3km[/tex] --- approximated

Ver imagen MrRoyal
raphealnwobi

The height of the airplane above the ground is 9.19 km.

Trigonometric ratio

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

Let h represent the height of the airplane above the ground. Hence:

sin(50) = h / 12

h = 9.19 km

The height of the airplane above the ground is 9.19 km.

Find out more on Trigonometric ratio at: https://brainly.com/question/1201366

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