(1) See below for a diagram. Basically, the distance on the ground from the person to the building (34 ft) is adjacent to the angle of elevation (74 degrees) and the height of the building (labeled h in the diagram) is the side opposite the angle. Since we are dealing with opposite and adjacent we use the tangent of the angle and tan = opp/adj
Specifically,


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feet.
Please be sure your calculator is set to degrees (not radians) when you do this problem.
(2) Here since P & Q are complimentary it means that their sum is 90 degrees. Since this is a right triangle that means that the remaining angle (R) must be the right angle. See below for a diagram.
sin = opp/hyp. As the sin Q = 9/41 this means that 9 is the length of the side opposite Q (the side PR) and 41 is the length of the hypotenuse. This makes the remaining side (QR) 40 in length.
cos = adj/hyp. If we focus on angle P the side adjacent (next to) is 9 and the hypotenuse is 41. Thus the cos of P = 9/41.
You could have also realized that if P & Q are complimentary the sin P = cos Q and the cos P = sin Q. We were not asked about tangent but it is also the case that tan P = cot Q and cot P = tan Q.
The sequence: a 1 = - 4, a 2 = 8, a 3 = -16,...
a 2 = a 1 * r
8 = - 4 * r
r = 8 : ( - 4 )
r = - 2
a n = a 1 * r^(n-1)
a 5 = - 4 * ( - 2 ) ^4 = - 4 * 16 = - 64
Answer:
The fifth term in the sequence is - 64.
the answer is D.
I dont know how to add work for a question like this, however, I know how I'd show work....
Draw a graph and stick a point in the IV quadrant and label it "original". Then next to it, draw another graph and stick a point in the III quadrant and label it "reflection"
TIP: if you do that, make sure the points are in the same location in each quadrant
11. 6:18 = 1:3
12. 12:48 = 1:4
13. 17:34 = 1:2
14. 8:64 = 1:8
15. 44:4 = 11:1
16. 121:11 = 11:1
17. 12:2 = 6:1
18. 4:2 = 2:1
19. 3:4 and 2:3 = 9:12 and 8:12
20. 1:6 and 3:14 = 7:42 and 9:42
21. 2:7 and 3:5 = 10:35 and 21:35
22. 5:2 and 3:1 = 5:2 and 6:2
Comparing Ratios:
1. 1.7 m = 170 cm
20:170 = 2:17
2. 160:8 = 20:1
3. 15:50 = 3:10
4. For every cup of milk she needs 5 cups of flour, so if she uses 3 cups of milk she'd need 15 cups of flour
Hopefully that helps :)