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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?
linebacker
left tackle
35
OA. 214 yards
OB. 26.2 yards
OC. 39.3 yards
17.9 yards
D.
15 yds
40°
right tackle

Select the correct answer. On a football field, the left and right tackles are lined-example-1
User Arafangion
by
7.8k points

2 Answers

2 votes

Final answer:

To determine the distance between the left and right tackles, the distances from each to the linebacker are calculated using trigonometry with the provided angles, and then summed. The result is approximately 23.09 yards, which aligns closest to option B, 26.2 yards.

Step-by-step explanation:

To find out how far apart the left and right tackles are, we can set up the problem using trigonometry, specifically by using the tangent function which relates angles to opposite and adjacent side lengths in a right triangle. The angles of sight of the tackles to the linebacker are given, as well as the distance of the linebacker from the yard line (15 yards). Assuming that the angles given are 40° and 35° for the right and left tackles respectively, we can calculate the horizontal distances from each tackle to the linebacker.

For the right tackle:

an(40°) = Opposite/Adjacent → Opposite = Adjacent × an(40°)

Distance from right tackle to linebacker = 15 yds × an(40°)

Similarly, for the left tackle:

an(35°) = Opposite/Adjacent → Opposite = Adjacent × an(35°)

Distance from left tackle to linebacker = 15 yds × an(35°)

To get the total distance between the tackles, we simply add these two distances:

Total distance = Distance from right tackle to linebacker + Distance from left tackle to linebacker

Using a calculator:

Distance from right tackle to linebacker ≈ 15 yds × 0.8391 ≈ 12.59 yards

Distance from left tackle to linebacker ≈ 15 yds × 0.7002 ≈ 10.50 yards

Total distance ≈ 12.59 yds + 10.50 yds ≈ 23.09 yards

Therefore, the correct answer is approximately 23.09 yards, which is closest to option B, 26.2 yards.

User Bartosz Gajda
by
7.8k points
2 votes

Answer:

Set your calculator to degree mode.

tan(40°) = 15/a

a = 15/tan(40°)

tan(35°) = 15/b

b = 15/tan(35°)

a + b = about 39.3 yards

The correct answer is C.

User Aaron Goldman
by
7.4k points