Multiple choice

The heights of two poles are $80$ m and $65$ m. If the line joining their tops makes an angle of $45^{\circ}$ with the horizontal, then the distance between the poles is :

  1. $15$ m
  2. $22.5$ m
  3. $30$ m
  4. $7.5$ m
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A Correct answer
Explanation

The difference in height between the two poles is 80 - 65 = 15 m. If the line joining the tops makes a 45-degree angle with the horizontal, the triangle formed by the height difference and the horizontal distance is an isosceles right triangle. Thus, the horizontal distance equals the height difference, which is 15 m.

AI explanation

The height difference between the two poles is 80 m minus 65 m, giving a vertical difference of 15 m. The line joining their tops makes a 45 degree angle with the horizontal, forming a right triangle where the height difference is the opposite side and the distance between the poles is the adjacent side. Using the tangent ratio, tan 45 = opposite divided by adjacent, which equals 1. Therefore, the distance between the poles is 15 m.

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