Acountertop is 18 feet long and 5 feet wide.

part 1 out of 2
what is the area of the countertop in square meters? use the conversion 1 foot = 0.305 meter. round your final answer to 2 decimal places.

the countertop is
square meters.

The countertop is  8.37 square meters

Step-by-step explanation:

Let

L ----> the length of the countertop

W ----> the width of the countertop

we know that

The area of rectangle (countertop) is equal to

we have

Remember that

To convert feet to meters multiply by 0.305

so

Find the area in square meters

Correct  cos(α - β) = 140/221

Step-by-step explanation:

cosα = ±√(1 - sin²α) => cosα = ±√(1 - (-5/13)²) = ±√(1 - (25/169)  

cosα = ±√(169 -25)/169 = ± √144/169

cosα = ± 12/13  since it is given that α (alpha) ends in the third quadrant

we choose  cosα = - 12/13

we know that is  tanβ = sinβ/cosβ = - 8/15 or sinβ : cosβ = 8 : 15 =>

sinβ = 8k and cosβ = 15k  where k is the coefficient of proportionality

we know the basic trigonometric equality

sin²β + cos²β = 1    when we replace the coefficients we get

(8k)² + (15k)² = 1 => 64k² + 225k² = 1 => 289k² = 1 => k² = 1/289 =>

k = 1/17   now we get sinβ and cosβ

since it is given that  β (beta) ends in the second quadrant

sinβ = 8/17 and cosβ = - 15/17

As we know it is:

cos(α - β) = cosα cosβ + sinα sinβ = - 12/13 · (- 15/17) + (- 5/13) · 8/17 =>

cos(α - β) = 180/221 - 40/221 = 140/221

cos(α - β) = 140/221

God is with you!!!