Multiple choice

From two points A and B on the same side of a building, that are in a straight line with it, the angles of elevation of the top of the building are 30° and 60° respectively. If the distance between the two points is 50 m, what is height of the building?

  1. 25.5 m

  2. 40.3 m

  3. 43.3 m

  4. 30.3 m
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let height be h. Distance from building is h/tan(60) and h/tan(30). The difference is h/tan(30) - h/tan(60) = 50. So h * (sqrt(3) - 1/sqrt(3)) = 50, which simplifies to h * (2/sqrt(3)) = 50, so h = 25 * sqrt(3) approx 43.3 m.

AI explanation

Let the height of the building be h and the distance from the closer point to the building be x, making the distance from the farther point x plus 50. Using the tangent ratio, tan 60 degrees equals h divided by x, which gives x equals h divided by the square root of 3. For the farther point, tan 30 degrees equals h divided by the quantity x plus 50, yielding x plus 50 equals h times the square root of 3. Substituting x and solving gives h times the square root of 3 minus h divided by the square root of 3 equals 50, which simplifies to h equals 25 times the square root of 3, or approximately 43.3 m.

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