Question

Problem 1. Consider a ladder of length 4 meters is placed against a wall. Suppose that the angle the ladder makes with the ground is 7/3. a) How far up the wall will the ladder reach (in meters)? b) What is the distance from the foot of the ladder to the base of the wall (in meters)?

Answer 1

Consider the ladder AB of length 4 meters placed against the wall. TT the angle that foot of ladder makes with ground is as shown below:

4 meters 001

now to find how far up the wall will the ladder reach, we use the trigonometric ratios for the right triangle ACB. observe that for the angle B, the opposite side is AC and adjacent side is BC, and the hypotenus is AB. so using the sine ratio, we know that, sin = sin opposite hypotenus -, so we have 6019E => AC = 4 x 3 → AC = 2V3 so the ladder will reach 2/3 meters up the wall.

adjacent Again using the cosine ratio, we know that cos = hypotenus So we have cos B = BC + BC = 4 x5 = BC = 2 thus, the distance from the foot of the ladder to base of the wall is 2 meters