Multiple choice

A straight highway leads to the foot of a tower ($AB$) of height $50\ m$. From the top of the tower, the angles of depression of two cars, $C\ and\ D$, standing on the highway are $30^o:and:60^o$. The first car is at a distance of $38.90\ m$ from the bottom of the tower.

  1. True

  2. False

Reveal answer Fill a bubble to check yourself
B Correct answer
AI explanation

The distance to the first car is found by using the tangent ratio in the right triangle formed by the tower and the highway. For an angle of depression of 60 degrees, tan(60) equals the tower height of 50 m divided by the distance of the car from the bottom. This gives a distance of 50 divided by the square root of 3, which is approximately 28.87 m. Because 28.87 m is not equal to 38.90 m, the statement is false.