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There is a tree in front of our yard. It is tilted slightly at 70°. Our house is 66 feet away from the tree. The
angle from our house to the top of the tree is 40°. Find the height of the tree.
Instruction: Illustrate and solve. Your output will be rated based on the rubrics below​

Sagot :

Problem:

  • There is a tree in front of our yard. It is tilted slightly at 70°. Our house is 66 feet away from the tree. The angle from our house to the top of the tree is 40°. Find the height of the tree.

Asked:

  • Find the height of the tree.

Solution:

In the triangle, we have assume height of tree is x ft.

[tex] \: \: \: \: \: \rm\frac{sin (∠B)}{AC} = \frac{sin (∠A)}{BC}[/tex]

  • ∠A = 180° - ∠B - ∠C

(The interior angles of a triangle sums 180°)

  • ∠A = 180° - 40° - 70° = 70°

[tex] \: \: \: \: \: \rm\frac{sin (40 \degree)}{x} = \frac{sin (70 \degree)}{66}[/tex]

[tex] \: \: \: \: \: \rm x = \frac{66 \: sin (40 \degree)}{ \sin(70 \degree) } [/tex]

  • x = 45.14666
  • x = 45.15

Answer:

  • The height of the tree is 45.15 ft
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