The angle of elevation of the top of a ladder leaning against a wall measured from a distance of 7.3 metres from the foot of the ladder is 45°. Suppose that the vertical height of the top of the ladder is 17.3 metres. Then the best approximation of the angle of inclination of the ladder with the wall is:

The foot of the ladder, its top against the wall, and the observation point form a right triangle where the horizontal distance is 7.3 meters and the vertical height is 17.3 meters. The angle of inclination of the ladder with the wall is theta, so tan theta equals the opposite side over the adjacent side, giving tan theta = 7.3 / 17.3. This ratio simplifies to approximately 0.421, which is very close to 1 / root 3. Therefore, theta is 30 degrees.

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