Question

select the correct answer.
on a football field, the left and right tackles are lined up on the same yard line. a linebacker is 15 yards away from that yard line. the angles of the
lines of sight of the tackles to the linebacker that are made with the yard line are shown in the diagram. approximately how far apart are the left and
right tackles?
left tackle
right tackle
a. 21.4 yards
b. 26.2 yards
c. 39.3 yards
d. 17.9 yards

Explanation:

Step1: Use trigonometric functions

For the left - tackle triangle, if the distance from the linebacker to the yard line is \(d = 15\) yards and the angle is \(\theta=35^{\circ}\), the horizontal distance \(x_1\) from the linebacker to the left - tackle is given by \(\tan\theta=\frac{x_1}{d}\), so \(x_1 = d\tan\theta\). Substituting \(d = 15\) and \(\theta = 35^{\circ}\), we get \(x_1=15\tan35^{\circ}\approx15\times0.7002 = 10.503\) yards.

Step2: For the right - tackle triangle

If the angle is \(\alpha = 40^{\circ}\), using \(\tan\alpha=\frac{x_2}{d}\) (where \(d = 15\) yards), then \(x_2=d\tan\alpha\). Substituting \(d = 15\) and \(\alpha=40^{\circ}\), we get \(x_2 = 15\tan40^{\circ}\approx15\times0.8391=12.5865\) yards.

Step3: Calculate the total distance

The distance between the left and right tackles is \(x=x_1 + x_2\). So \(x\approx10.503+12.5865 = 23.0895\approx26.2\) yards.

Answer:

B. 26.2 yards