Problema Solution
a 16 meter ladder is placed against a vertical wall while the other end of the ladder reaches a point on the floor 7 meter from the wall. Find the sine, cosine and tangent of the angle that the ladder makes (a) with the wall; (b) with the floor
Answer provided by our tutors
make a drawing: the ladder, the wall and the floor are sides of a right triangle
for this right triangle we know that one leg is a = 7 meters and the hypotenuse is c = 16 meters
using the Pythagorean Theorem we find the other leg b = (16^2 - 7^2)^0.5 = 207^0.5 = 14.39
(a) with the wall;
< A = the angle of the ladder with the wall
sine (< A) = 7/16
sine (< A) = 0.4375
cosine (< A) = 14.39/16
cosine (< A) = 0.899375
tangent (< A) = 7/14.39
tangent (< A) = 0.48645
(b) with the floor
< B = the angle of the ladder with the floor
cosine (< B) = 7/16
cosine (< B) = 0.4375
sine (< B) = 14.39/16
sine (< B) = 0.899375
tangent (< B) = 14.39/7
tangent (< B) = 2.05571