Answer :
Final answer:
To find the distance from the bear to the base of the tower, we can use trigonometric ratios. By using the tangent ratio and the given angle of depression, we can calculate the distance using the height of the tower.
Explanation:
To find the distance from the bear to the base of the tower, we can use trigonometric ratios.
Let x be the distance from the bear to the base of the tower.
Since the angle of depression to the bear is 62°, we can use the tangent ratio.
Tan(62°) = Opposite/Adjacent. The opposite side is the height of the tower (14 m) and the adjacent side is the distance from the bear to the base of the tower (x).
Tan(62°) = 14/x
Using inverse tangent, we can solve for x.
x = 14/Tan(62°)
Using a scientific calculator, we can find that x is approximately 26.3 m.
Final answer:
Using trigonometry, specifically the tangent of the angle of elevation, the distance from the bear to the base of a 14 m tower is approximately 12.4 m, which corresponds to Option B.
Explanation:
The question involves using trigonometry to find the distance from a bear to the base of a tower. Since the angle of depression from the top of the tower to the bear is given as 62°, we can use this angle to calculate the horizontal distance to the bear. The angle of depression is equal to the angle of elevation from the bear to the observer because these are alternate interior angles created by a horizontal line (the observer's line of sight) and parallel to the ground (the horizontal line).
The correct answer is Option B, 12.4 m.