Recall the sum identity for cosine:
cos(a + b) = cos(a) cos(b) - sin(a) sin(b)
so that
cos(a + b) = 12/13 cos(a) - 8/17 sin(b)
Since both a and b terminate in the first quadrant, we know that both cos(a) and sin(b) are positive. Then using the Pythagorean identity,
cos²(a) + sin²(a) = 1 ⇒ cos(a) = √(1 - sin²(a)) = 15/17
cos²(b) + sin²(b) = 1 ⇒ sin(b) = √(1 - cos²(b)) = 5/13
Then
cos(a + b) = 12/13 • 15/17 - 8/17 • 5/13 = 140/221
Answer:
809 km²
Step-by-step explanation:
I can split this into 3 rectangles. One is 25 by 17, another is 24 by 13, and the last one is 6 by 12. (I had gotten 13 for the second rectangle because 25 - 12 = 13.)
(25 * 17) + (24 * 13) + (6 * 12) <em>{17 is the first number after a multiple of 4 (16). As a result, 25 by 17 will end in "25." 25 by 17 is 425.}</em>
425 + (24 * 13) + (6 * 12) <em>{24 by 13 is 312.}</em>
425 + 312 + (6 * 12) <em>{6 by 12 is 72.}</em>
425 + 312 + 72 <em>{From left to right, add 425, 312, and 72 to get 809}</em>
737 + 72
809 km²
The area of this figure is 809 km².
Answer: hope this helps .
Step-by-step explanation: