Multiple choice

Two housed are collinear with the base of a tower and are at distances 3 m and 12 m ( on the same side ) from the base of the tower. The angles of elevation form these two houses of the top of the tower are complementary. what is the height of the tower?

  1. 4 m

  2. 6 m

  3. 7.5 m

  4. 36 m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The tangents of the two complementary angles are h/3 and h/12, where h is the tower height. Their product is 1, so h^2/36 = 1 and h = 6 m.

AI explanation

Let the height of the tower be h. If the angles of elevation from distances of 3 meters and 12 meters are complementary, we can use the tangent identity to get h squared equals the product of the two distances. Therefore, h squared equals 3 multiplied by 12, which is 36. Taking the square root gives a tower height of 6 meters.

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