Question

A ladder leans against the side of a house. The angle of elevation of the ladder is 66 degrees when the bottom of the ladder is 16ft from the side of the house. Find the length of the ladder. Round your answer to the nearest tenth.

Answer 1

Answer:

The length of the ladder  = 6.5077 ft

Step-by-step explanation:

Given A ladder leans against the side of a house

Given the angle of elevation of the ladder is 66° when the bottom of the ladder is 16 ft from the side of the house

Let 'C' be the point of observation.

Given CA= 16 ft

  From right angle triangle

      $cos C = \frac{CB}{CA}$

     $cos 66 = \frac{x}{16}$

      x = 16 × cos 66°

     x = 16 × 0.4067

     x = 6.5077

   x = 6.5 ft

The length of the ladder = 6.5 ft