I don't think its right . can you correct me please .
A.log sin A = 9.91655 - 10
sinA = 0.82537
A = 55.626° = 55° 34' 35"
B.log cot A = 0.11975
cot(A) = 1.317498...
A = 37.199 degs
A = 37º 11' 56"
What is the logarithm base? e or 10 ?
I was just off by a bit from yours on the first, don't round off too soon, since you are using a calculator, use all the decimals till the very end
log sin A = 9.91655 - 10
log sin A = -.08345
sin A = .825182
A = 55° 36' 25"
the second is correct.
Thank you !
To correct your answers, let's work through the calculations.
For Part A, you correctly started by taking the logarithm of both sides of the equation log sin A = 9.91655 - 10. However, there seems to be an error in the value you provided for the right-hand side of the equation (9.91655 - 10).
Assuming the correction means subtracting 10 from 9.91655, we would have:
log sin A = -0.08345
Next, to find the value of sin A, we need to undo the logarithm by taking the exponentiation of both sides:
10^(log sin A) = 10^(-0.08345)
sin A = 0.9491
Now, to find the angle A, we can use the inverse sine function (also known as arcsine):
A = arcsin(0.9491)
A ≈ 69.434 degrees
To convert to degrees, minutes, and seconds, we can use the following conversions:
69.434 * 60 = 4166.4 (multiply by 60 to convert to minutes)
0.4 * 60 = 24 (multiply the decimal part by 60 to convert to seconds)
Therefore, A is approximately equal to 69 degrees 41 minutes 24 seconds.
For Part B, you started by taking the logarithm of both sides of the equation log cot A = 0.11975. However, there is an error in the value you provided for the logarithm.
Assuming the correction means taking the logarithm of 0.11975, we would have:
log cot A = -0.92010
Next, to find the value of cot A, we need to undo the logarithm by taking the exponentiation of both sides:
10^(log cot A) = 10^(-0.92010)
cot A ≈ 0.4074
Now, to find the angle A, we can use the inverse cotangent function (also known as arccotangent):
A = arccot(0.4074)
A ≈ 66.967 degrees
To convert to degrees, minutes, and seconds, we can use the following conversions:
66.967 * 60 = 4018.2 (multiply by 60 to convert to minutes)
0.2 * 60 = 12 (multiply the decimal part by 60 to convert to seconds)
Therefore, A is approximately equal to 66 degrees 59 minutes 12 seconds.