Question

Please help me do this

Answer 1

Answer: below!

Explanation:

9: tan51 = 8/x

x = 8/(tan51) ≅ 6.478

10: sin24 = x/31

.: x = 31sin24 ≅ 12.609

11: You've done it correctly!

12: tanx = 25/78

.: x =
`tan^-^1((25)/(78) )` ≅ 17.77°

15: Correct!

16: sin25 = 15/(XZ)

.: XZ = 15/sin25 ≅ 35.5

Since triangle WXZ is right, the pythagorean theorem tells us that WZ =
`√(22^2 + 35.5^2)` ≅ 41.76

Now, using the Law of Sines, we can say that sin90/WZ = sinW/XZ

this means 1/41.76 = sinW/35.5

W =
`sin^-^1((35.5)/(41.76) )` ≅ 58.2°

17. Draw this image. You'll see a right triangle, with angles 90-75-15. Since the side adjacent to the 75 deg angle is 6, we can solve for the length of the ladder. in essence:

cos75 = 6/x, where x is the length of the ladder

.: x = 6/cos75 ≅ 23.18 feet