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Florence stands in her backyard and admires her flower gardens. First, she looks to her rose garden. Her rose garden is 80 feet away from her. She turns 63° and views where she has lilies planted. The lily garden is 140 feet away from her. How far apart are the rose garden and the lily garden?

Respuesta :

Answer:

The rose garden is 125.82 feet apart from the lily garden.

Step-by-step explanation:

See the attached diagram.

The position of Florence is A and the position of the rose garden and the lily garden forms a triangle Δ ARL.

Now, from the property of triangle, we can write

x² = 80² + 140² - 2 × 140 × 80 × Cos 63°

⇒ x² = 15830.61

⇒ x = 125.82 feet.

Therefore, the rose garden is 125.82 feet apart from the lily garden. (Answer)

Ver imagen rani01654

The distance between the rose garden and lily garden is 125.82ft

Data;

  • a = 80ft
  • b = 140ft
  • angle = 63 degree
  • c = ?

Cosine Rule

To find the distance between the two flowers, we can use cosine rule which is given as

[tex]c^2 = a^2 + b^2 -2abcosC[/tex]

Let's substitute the values and solve the equation

[tex]c^2 = 80^2 + 140^2 - 2*80*140*cos63\\c^2 = 6400+19600 - 10169.38\\c^2 = 15830.62\\c = \sqrt{15830.62}\\ c = 125.82ft[/tex]

The distance between the rose garden and lily garden is 125.82ft

Learn more on cosine rule here;

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