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36 votes
36 votes
Jaxon is flying a kite, holding his hands a distance of 3.25 feet above

the ground and letting all the kite's string play out. He measures the
angle of elevation from his hand to the kite to be 24°. If the string from
the kite to his hand is 105 feet long, how many feet is the kite above the
ground? Round your answer to the nearest tenth of a foot if necessary.

User Minchul
by
2.8k points

2 Answers

24 votes
24 votes

Final answer:

To find the height of the kite, first calculate the height component by using the sine of the angle of elevation with the string length and then add Jaxon's hand height. The kite is approximately 46.0 feet above the ground.

Step-by-step explanation:

The question involves using trigonometric principles to find the height of a kite above the ground. Given that Jaxon is holding the kite string at a height of 3.25 feet above the ground and the string is 105 feet long with an angle of elevation of 24°, we can use the sine trigonometric ratio to solve for the height of the kite.

To find the height of the kite above the ground, we perform the following calculation:

  1. Calculate the height from Jaxon's hands to the kite using the sine of the angle of elevation: height = 105 feet × sin(24°).
  2. Add Jaxon's hand height above the ground to the height calculated in the previous step.

By performing the calculation:

height = 105 feet × sin(24°) = 105 × 0.4067 ≈ 42.7 feet

Now we add Jaxon's hand height to the height of the kite:

Total height above ground = 42.7 feet + 3.25 feet ≈ 45.95 feet

Rounded to the nearest tenth of a foot, the kite is approximately 46.0 feet above the ground.

User Erynn
by
3.0k points
5 votes
5 votes

Answer:

Step-by-step explanation:

105

105

x

sin

24

1

=

1

sin 24

=

105

105

x

105

sin

24

=

105 sin 24=

x

Cross multiply.

=

42.707347...

x=42.707347...

Type into calculator.

Add 3.25, the distance from the ground to his hand:

Add 3.25, the distance from the ground to his hand:

42.707347...

+

3.25

=

42.707347...+3.25=

45.957347...

45.957347...

46

46

Round to the nearest tenth.

The kite is 46 feet above the ground.

The kite is 46 feet above the ground.

User Mohammad Efazati
by
3.1k points