Step-by-step explanation:

Answer:
78°
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relations between angles and sides of a right triangle. In particular, ...
Cos = Adjacent/Hypotenuse
cos(F) = FG/FE = 1.5/7.5 = 0.2
The inverse cosine function is used to find the angle:
∠F = arccos(0.2)
∠F ≈ 78°
Answer:
1.601 x 10^9
Step-by-step explanation:
Answer:
19 nails
Step-by-step explanation:
Let's first determine the z-score by using the formula:

Where x=5.03, μ=5, σ=0.03 and so:

We can now use a z-score table to determine that 1.00 is synonymous with 0.8413 meaning 84.13%. This means that 84.13% of the nails are less than or equal to 5.03 inches long. Therefore, since we know 100% = 1 in decimals we can determine that the length greater than 5.03 inches is 1-0.8413=0.1587. This means that 15.87% of the 120 nails are greater than 5.03 inches long.
Finally, we can determine how many nails are greater than 5.03 by determining what is 15.87% of 120 which is:

And so 19 out of the 120 nails are greater than 5.03 inches long.