Answer:
3a. 35°, 55° 3b. 36°, 54°
Step-by-step explanation:
3a. sin(3x + 2)° = cos(x+44)°
Since sine and cosine are based upon right triangles, the two angles must add up to 90°. Thereby, 3x+2 + x+44 = 90. Combine like terms to get:
4x + 46 = 90 subtract 46 from both sides
-46 -46
4x = 44 divide both sides by 4
4 4
x = 11 plug that back into both angles
3(11) + 2 = 35°; 11 + 44 = 55°
3b. In your equation, (2x+20) + (3x+30) = 90. Combining like terms gives you:
5x + 50 = 90 subtract 50 from both sides
<u> - 50 -50</u>
<u>5x = 40</u> divide both sides by 5
5 5
x = 8 plug that back into both angles
2x+20 = 2(8) + 20 = 36°
3x+30 = 3(8) + 30 = 54°
The two angles are 36° and 54°
