lorna1717
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During a figure skating routine, Jackie and Peter skate apart with and angle of 15 degrees between them. Jackie skates for 5 meters, and Peter skates for 7. How far apart are the skaters?

Respuesta :

Answer:

The skaters are 2.5 feet apart

Step-by-step explanation:

Firstly, please check attachment for diagrammatic representation.

To calculate the distance apart, this is same as the length PJ

To calculate this length, we can use the cosine rule as follows;

O^2 = P^2 + J^2 -2(P)(J)Cos 15

O^2 = 7^2 + 5^2 -2(7)(5)Cos 15

O^2 = 49 + 25 - 70Cos15

O^2 = 74 - 67.61

O^2 = 6.39

O = √6.39

O = 2.53

O = 2.5 feet to the nearest tenth of a foot

Ver imagen Adetunmbiadekunle

The distance between the skaters is 2.5m

Data;

  • Jackie (a) = 5m
  • Peter (b) = 7m
  • angle = 15 degrees
  • distance apart = c

Cosine Rule

To solve this problem we can use cosine rule for this since we have the value of two sides and an angle.

[tex]c^2 = a^2 + b^2 -2ab cos C[/tex]

Let's substitute the values into the formula

[tex]c^2 = 5^2 + 7^2 - 2*5*7*cos15\\c^2 = 25 + 49 - 67.61\\c^2 = 6.39\\c = \sqrt{6.39} \\c = 2.5m[/tex]

The distance between the skaters is 2.5m

Learn more on cosine rule here;

https://brainly.com/question/4372174