MathMate i would really appreciate

if you can show me where the logarithms can be used.I know they are unnecessary and I already found the answer without them but i still have to show my work using logarithms and they just confuse me. I also have most trouble woth the anti-logarithm.
I am seriously frustrated so you help would be appreciate.
I hope my repost is okay because i wasn't sure if you would go back and check the older post.

Find the area of the following triangles:(use logarithms)

1) c=426, A=45degrees 48' 36",and B=61degrees 2' 13"

It is perfectly to repost with a reference to an earlier post.

Here it is:

Given triangle,
A=45-48-36
B=61-02-13
c=426
C=180-00-00 - (45-48-36 + 61-02-13) = 73-09-11

Solve by the sine rule:
a/sin(A)=c/sin(C)
a=c*sin(A)/sin(C)

value logarithm
c 2.6294096
sin(A) 1̅.8555387
c*sin(A) 2.4849483 [ADD]
sin(C) 1̅.9809493
a 2.5039990 [SUBTRACT]
Anti-log 319.1530 (length of c)

Now proceed to calculate area:

Area = (1/2)a*c*sin(B)

value logarithm
(1/2) 1̅.6989700
a 2.5039990
c 2.6294096
sin(B) 1̅.9419744
Area 4.774353 [ADD]
Anti-log 59477.54

Note:

when a number is between 1 and 10, it is normalized, and the logarithm (to the base 10) is between 0 and 1.
Example: log(2) = 0.30103

However, when the number is less than 1, such as 0.5, the decimal is moved one place to the left, and log(5) is recorded (.6989700) with a 1̅ to the left meaning the decimal has been move one to the left.

Conversely, the logarithm of 50 is written simply as 1.6989700, meaning log(5) with one decimal placed to the right.

If you need more details, post (here).

okay i was able to get

c*sin(A)= 1.8555387
but i was lost after that. I couldn't reproduce the same answers u have.

value logarithm
c 2.6294096
sin(A) 1̅.8555387
2.4849483 [ADD]
sin(C) 1̅.9809493
a 2.5039990 [SUBTRACT]
Anti-log 319.1530 (length of c)

Are you able to get the individual logarithms?

For example,
A=45.81°
sin(A)=0.7170323
sin(A)*10=7.170323 (normalize number to between 1 and 10)
Log(sin(A)*10)=0.855387
To move the decimal back one place to the left, we put a (-1) denoted by 1̅ which makes
log(sin(A))=1̅.855387

The we add (instead of multiply) the logarithms
c 2.6294096
sin(A) 1̅.8555387
2.4849483 [ADD]

which is
2.6294096+(-1)+.855387
=2.4849483
Note that the mantissa (the decimal part of the log) is always positive. The characteristics (integer part) are always added separately, and do remember to add the carries, if any.

The subtraction would be calculated similarly.

Please post again if you need more details.

I'm sorry to hear that you're feeling frustrated with logarithms, but I'm here to help! Logarithms are actually incredibly useful in a wide range of mathematical calculations, especially when dealing with exponential growth or decay, solving equations involving exponents, or when working with large or small numbers. They are commonly used in fields such as science, engineering, and finance.

In the case of finding the area of triangles, logarithms might not be necessary. However, if you're specifically asked to use logarithms to show your work, I can guide you through the process.

To find the area of a triangle using logarithms, you would typically use the formula:

A = 0.5 * c * a * sin(B)

Where:
A represents the area of the triangle,
c is the length of one side,
a is the length of another side,
and B is the angle between these two sides.

In your case, the given information is:
c = 426
A = 45 degrees 48' 36" (converted into decimal degrees, this would be 45.8100 degrees)
B = 61 degrees 2' 13" (converted into decimal degrees, this would be 61.0369 degrees)

Now, let's go through the steps using logarithms:

Step 1: Convert the angles from degrees, minutes, and seconds to decimal degrees.

To convert 48' 36" into decimal degrees, divide 48 by 60 and add it to 36 divided by 3600. This gives us:
48/60 + 36/3600 = 0.8 + 0.01 = 0.81 degrees

Similarly, for 2' 13":
2/60 + 13/3600 = 0.0333 + 0.0036 = 0.0369 degrees

Now we have:
A = 45.8100 degrees
B = 61.0369 degrees

Step 2: Use the formula for the area of a triangle:

A = 0.5 * c * a * sin(B)

Step 3: Substitute the given values into the formula:

A = 0.5 * 426 * a * sin(61.0369)

Step 4: Now, we need to find the value of 'a'. Rearrange the formula to solve for 'a':

a = (2 * A) / (c * sin(B))

Step 5: Substitute the known values into the equation:

a = (2 * 45.8100) / (426 * sin(61.0369))

Step 6: Use a scientific calculator to find the value of sin(61.0369), which is approximately 0.8720.

a = (2 * 45.8100) / (426 * 0.8720)

a ≈ 0.2308

Now you have the value of the second side, 'a', which is approximately 0.2308. With this value, you can calculate the area of the triangle using the formula A = 0.5 * c * a * sin(B).

Remember, logarithms were not necessary to find the numerical value, but if you're asked to include logs in your calculations, you could use them to evaluate expressions involving trigonometric functions or to find the values of sin, cos, or tan.

I hope this step-by-step explanation helps you in understanding how to use logarithms to find the area of a triangle, even though they might not be needed in this specific case. If you have any further questions, please let me know!