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Use the triangle to answer the question. In the triangle, the length of side a is 5 ft., and m ∠ A = 60 ° . Find the exact lengths of sides b and c. Please show work.

Use the triangle to answer the question In the triangle the length of side a is 5 ft and m A 60 Find the exact lengths of sides b and c Please show work class=

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mhanifa

Answer:

  • b = 5√3/3 or ≈ 2.9
  • c = 10√3/3 or ≈ 5.8

Step-by-step explanation:

This is a 30°-60°-90° triangle

  • ∠A is 60°, so ∠B is 30°

Given also:

  • a = 5 ft

As per property of  30°-60°-90° triangle, the ratio of sides is:

  • b : a : c = 1 : √3 : 2

Since a = 5, the missing sides are:

  • b/a = 1/√3  ⇒ b = a/√3 = 5/√3 = 5√3/3 ≈ 2.9
  • b/c = 1/2 ⇒ c = 2b = 10√3/3 ≈ 5.8

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