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A chandelier is suspended from the ceiling by two chains. one chain is 46cm long and forms an angle of 60o with the ceiling. the other chain 64cm long. what angle does the longer chain make with the ceiling?

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The angle the longer chain makes with the ceiling is 38.5°

The two chains and ceiling form a triangle and with two sides and an angle, we use the sine rule to find the other angle

What is the sine rule?

The sine rule states in any triangle with sides a, b, c and angles A, B and C, repsectively, we have that

a/sinA = b/sinB = c/sinC

Since one chain is 46cm long and forms an angle of 60° with the ceiling. the other chain 64cm long. So, we find the other angle.

So, a/sinA = b/sinB  where

  • a = 46 cm,
  • b = 64 cm
  • A = other angle
  • B = 60°

The value of the other angle

Making A subject of the formula, we have

A = sin⁻¹(asinB/b)

So, substituting the values of the variables into the equation, we have

A = sin⁻¹(asinB/b)

A = sin⁻¹(46 cm × sin60/64 cm)

A = sin⁻¹(46 cm × 0.8660/64 cm)

A = sin⁻¹(39.84 cm/64 cm)

A = sin⁻¹(0.6225)

A = 38.49°

A ≅ 38.5°

So, the angle the longer chain makes with the ceiling is 38.5°

Learn more about sine rule here:

https://brainly.com/question/27174058

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