Question

A 10-foot board rest against a wall. the angle that the board makes with the ground is 60 degrees. how far is the base of the board away from the wall?

Select the correct Trig ratio and distance from wall?

Answer 1

Answer: cos 60 = x/10; x= 5 feet

Answer 2

The base of the board away from the wall is 5 foot .

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.

`cos \theta = (Base)/(Hypotenuse)`

As shown in the figure given below.

`\theta = 60^(\circ)`

Base = CB

Hypotenuse = AC = 10 foot

Put in the identity

`cos\ 60^(\circ) = (BC)/(AC)`

`cos\ 60^(\circ) = (BC)/(10)`

`cos\ 60^(\circ) = 0.5`

Put in the above

`0.5= (BC)/(10)`

BC = 10 × 0.5

BC = 5 foot

Therefore the base of the board away from the wall is 5 foot .