Question

ray and terry both calculated the height of the partition as shown.
rays calculation
\\( \sin ( 30 ^ { \circ } ) = \frac { \text { height } } { 35 } \\)
\\( \text { height } = 35 \cdot \sin ( 30 ^ { \circ } ) \\)
\\( = 17.50 \text { inches } \\)
terrys calculation
\\( \tan ( 30 ^ { \circ } ) = \frac { \text { height } } { 35 } \\)
\\( \text { height } = 35 \cdot \tan ( 30 ^ { \circ } ) \\)
\\( \approx 20.21 \text { inches } \\)
examine ray and terrys calculations and complete the given statement.
the person with the incorrect reasoning for the height of the partition is \\( \vee \\) because he incorrectly selected the \\( \vee \\) function.
when he should have utilized the \\( \vee \\) function.

Explanation:

Step1: Analyze Ray's calculation

Ray used the sine function. In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, if we consider the angle \(30^{\circ}\), the height is the opposite side and the given side (35 inches) is the hypotenuse. So, \(\sin(30^{\circ})=\frac{\text{Height}}{35}\), and \(\text{Height}=35\times\sin(30^{\circ})\). Since \(\sin(30^{\circ}) = 0.5\), \(\text{Height}=35\times0.5 = 17.5\) inches.

Step2: Analyze Terry's calculation

Terry used the tangent function. In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). But in the given problem, we know the hypotenuse (35 inches) and we want to find the opposite side (height). The tangent function relates the opposite and adjacent sides. Terry should have used the sine function instead of the tangent function.

Answer:

The person with the incorrect reasoning for the height of the partition is Terry because he incorrectly selected the tangent function.