Question

select the correct answer from each drop - down menu. ray and terry work in the same office. they sit across from each other at fixed desks that are separated by a partition, or a short dividing wall, exactly halfway between them. the distance between the end of each desk and the partition is 35 inches. for both ray and terry, the top of the partition is at an angle of elevation of 30° with respect to the end of the desk. this scenario can be modeled by the given diagram. ray and terry both calculated the height of the partition as shown. examine ray and terrys calculations and complete the given statement. the person with the incorrect reasoning for the height of the partition is ray, because he incorrectly selected the function, when he should have utilized the function.

Explanation:

Step1: Recall trigonometric ratios

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\) and \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\).

Step2: Analyze Ray's calculation

Ray used \(\sin(30^{\circ})=\frac{\text{Height}}{35}\). But in the right - triangle formed (angle of elevation \(30^{\circ}\), adjacent side \( = 35\) inches, opposite side \(=\text{Height}\)), the correct ratio is \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\).

Step3: Analyze Terry's calculation

Terry used \(\tan(30^{\circ})=\frac{\text{Height}}{35}\), which is correct as \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\) where \(\theta = 30^{\circ}\), adjacent \(=35\) inches and opposite \(=\text{Height}\).

Answer:

The person with the incorrect reasoning for the height of the partition is Ray, because he incorrectly selected the sine function, when he should have used the tangent function.