Use logarithms and the law of tangents to solve the triangle ABC, given that a=21.46 ft, b=46.28 ft, and C=32°28'30"
I have to use logarithms and law of tangents . and then provide the check.
which says law of sine or mollweids equation. I can't us the cosine law.
If you already posted the responds then please provide me with the link.
I have posted a corrected version of solution using the law of tangents.
I believe by now you are capable of doing the calculations (multiplications and divisions) using logarithms.
I found the third side (c) using the cosine rule, but it gives the same answer as the sine rule, similar to what you did.
Here's the link to your original post:
http://www.jiskha.com/display.cgi?id=1298609593
To solve the triangle ABC using logarithms and the law of tangents, follow these steps:
1. Calculate c:
- Use the law of tangents: tan(C) = b / a
- Convert the angle C from degrees, minutes, and seconds to decimal degrees: C = 32 + 28/60 + 30/3600
- Substitute the values: tan(32°28'30") = 46.28 ft / 21.46 ft
- Use logarithms to solve for C: C = arctan(46.28 ft / 21.46 ft)
2. Calculate angle A:
- Use the law of tangents: tan(A) = c / b
- Substitute the calculated value for c and the given value for b: tan(A) = C / 46.28 ft
- Use logarithms to solve for A: A = arctan(C / 46.28 ft)
3. Calculate angle B:
- Angle B can be found by subtracting angles A and C from 180 degrees: B = 180° - A - C
Now that you have found the angles, you can also check your solution using the law of sines or the Mollweid's equation:
Law of Sines:
- Calculate the ratio of the sides: sin(A) / a = sin(B) / b = sin(C) / c
- Substitute the known values: sin(A) / 21.46 ft = sin(B) / 46.28 ft = sin(C) / c
- Calculate the missing side length using the known angles:
- For side a: a = sin(A) / sin(C) * c
- For side b: b = sin(B) / sin(C) * c
Mollweid's Equation:
- Calculate the following value: cos((A + B) / 2) = cos(C / 2)
- Use logarithms to solve for A and B: A = 2 * arccos(cos(C / 2)) - C, B = 2 * arccos(cos(C / 2)) - A
Please note that the exact calculations with logarithms might be time-consuming and require a calculator with logarithmic functions.