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? a. 39.3 yards b. 17.9 yards c. 21.4 yards d. 26.2 yards

Explanation:

Step1: Find left tackle's horizontal distance

Let $x$ = left horizontal segment. Use $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$:
$\tan(35^\circ)=\frac{15}{x} \implies x=\frac{15}{\tan(35^\circ)}$
Calculate: $x\approx\frac{15}{0.7002}\approx21.42$ yards

Step2: Find right tackle's horizontal distance

Let $y$ = right horizontal segment. Use $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$:
$\tan(40^\circ)=\frac{15}{y} \implies y=\frac{15}{\tan(40^\circ)}$
Calculate: $y\approx\frac{15}{0.8391}\approx17.88$ yards

Step3: Sum distances for total separation

Total distance = $x + y$
<Expression>
$21.42 + 17.88 = 39.3$ yards

Answer:

A. 39.3 yards