CALCULATING ANGLES

Question

A 3m ladder is leaning against a vertical wall with its foot 1,5m from the base of the wall. How high does the top of the ladder reach and what angle does the ladder make with the floor if its angle with the wall is 52‚º?

Answer 1

The triangle formed by the ladder leaning against the wall will be a right triangle (the 90 degree angle being where the floor meets the wall). The sum of the angles of a triangle must equal 180 degrees. Let the unknown angle between the ladder and the floor be x. Then, the three angles in the triangle are 90, 52, and x. Thus,

90 + 52 + x = 180

142 + x = 180

x = 38

The ladder will be the hypotenuse of the triangle and has length 3m. One of the sides of the triangle is 1.5m. Using the Pythagorean Theorem to determine the unknown side, y, of the triangle (and thus the height that the ladder reaches on the wall):

(1.5 m)² + y² = (3 m)²

y² = (3 m)² - (1.5 m)²

y² = 9 m² - 2.25 m²

y² = 6.75 m²

y = √(6.75 m²)

y ≈ 2.60 m