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A 20-meter line is used to keep a weather balloon in place. The sine of the angle that the line makes with the ground is 3/4. How high is the balloon in the air?

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Respuesta :

To find how high the balloon is in the air, given the length of the line and the sine of the angle, we can use the trigonometric function sine.

Given:
- The length of the line is 20 meters.
- The sine of the angle is 3/4.

The sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Therefore, the height \( h \) of the balloon can be calculated as follows:

\[ \sin \theta = \frac{h}{20} \]

Given that the sine of the angle is 3/4, we substitute and solve for \( h \):

\[ \frac{3}{4} = \frac{h}{20} \]

To solve for \( h \), multiply both sides by 20:

\[ h = \frac{3}{4} \times 20 \]
\[ h = 15 \]

Therefore, the balloon is 15 meters in the air.
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Answer:

  • 15 m

Step-by-step explanation:

Given:

  • A 20-meter line is used to keep a weather balloon in place. The sine of the angle that the line makes with the ground is 3/4.

To Calculate:

  • The height of the balloon ,

To Calculate the height of the balloon, we can use the sine function.

  • The sine function can be defined as the ratio of the length of the opposite side to that of the hypotenuse in a right-angled triangle.

[tex]\sin \theta = \sf \dfrac{opposite} {hypotenuse}[/tex]

From the figure,  

  • Opposite (The height of the balloon) = h
  • Hypotenuse (The length of the line which is used to keep a weather balloon in place) = 20 m
  • [tex]\sin  \theta = \dfrac{3}{4} [/tex]

Substitute the values,

[tex]\dfrac{3}{4} =  \dfrac{h}{\sf {20}}[/tex]

[tex]{\sf {h}} = 20 \times \dfrac{3}{4} [/tex]

[tex]{\sf {h }}= 15 \ {\sf{m }}[/tex]

[tex]\therefore[/tex] The height of the balloon is 15 m

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