Answer to Question #20451 in Analytic Geometry for Caleb Stamper

Question

x represents the length of a ladder leaning up against a wall of a building, and y represents the length from the base of the wall to the bottom of the ladder. The ladder makes a 60 degree angle with the ground and reaches a point on the wall 17 feet above the ground. Find the number of feet in x and y. Round to the nearest tenth of a foot.

Answer 1

Here is the expression that relates x, y and α (angle the ladder makes with the ground):

tg(α) = y/x (1)

As the ladder reaches a point on the wall 17 feet above the ground, then obviously x = 17[ft]. Therefore,

(1) ==> y = tg(α)·x = tg(60°)·17[ft] = √3·17[ft] ≈ 29.4[ft].

So, x value is 17 feet and the y value is about 29.4 feet.