17) describe the gulf of guinea:

The Gulf of Guinea is the north easternmost part of the tropical Atlantic Ocean between Cape Lopez in Gabon, north and west to Cape Palmas in Liberia. ... Among the many rivers that drain into the Gulf of Guinea are the Niger and the Volta. The coastline on the gulf includes the Bight of Benin and the Bight of Bonny

Explanation:

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!!!