Question

A wooden plank is leaning against a wall. The bottom of the plank is 3 feet from the wall. Answer each of the following questions, and show all your work.
(a) Find AC, the approximate length of the plank. Round to the nearest tenth of a foot.

(b) Find BC, the height off the ground where board touches as wall. Round to the nearest foot.

Answer 1

AB = ==> distance between the bottom of the plank; and the wall ===> 3 ft.

C ====> 49 degrees

For letter a, to solve for AC:

AC ==> HYPOTENUSE. The angle C is the OPPOSITE side of AB.

use sine :

sin A ===> opposite/hypotenuse

Solve:

sin 49 ====> 3/AC

AC ====> 3 / sin 49

AC ====> 3.96 ft.

For letter b, to solve for BC:

We are now given with the base (3 ft.); and; the hypotenuse (3.96 ft.) so we can use the Pythagorean theorem:

a^2 + b^2 = c^2

Let:

a ===> AB

b ===> BC

c ===> AC

(AB)^2 + (BC)^2 ===> (AC)^2

3^2 + (BC)^2 ===> (3.96)^2

(BC)^2 ===> (3.96)^2 - 3^2

(BC)^2 ===> 6.6816

sqrt (BC)^2 ===> sqrt 6.6816

Answer: BC ===> 2.58 ft.

Hope that helps!!!! : )