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
<h3>What is the sine rule?</h3>
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°
<h3>The value of the other angle</h3>
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:
brainly.com/question/27174058
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