Answer:
The base of the board away from the wall is 5 foot .
Step-by-step explanation:
As given
A 10-foot board rest against a wall. the angle that the board makes with the ground is 60 degrees.
Now by using the trigonometric identity.
[tex]cos \theta = \frac{Base}{Hypotenuse}[/tex]
As shown in the figure given below.
[tex]\theta = 60^{\circ}[/tex]
Base = CB
Hypotenuse = AC = 10 foot
Put in the identity
[tex]cos\ 60^{\circ} = \frac{BC}{AC}[/tex]
[tex]cos\ 60^{\circ} = \frac{BC}{10}[/tex]
[tex]cos\ 60^{\circ} = 0.5[/tex]
Put in the above
[tex]0.5= \frac{BC}{10}[/tex]
BC = 10 × 0.5
BC = 5 foot
Therefore the base of the board away from the wall is 5 foot .
