If you're looking for the dashed line, here it is.
<span>Answer:
Use properties of logarithm to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using calculator.
log4(4/x) = log4(4) - log4(x) = 1 - log4(x)
------------------------------------------------------
Evaluate the expression without using a calculator.
log7 1/root:7
log7(1/sqrt(7))
= log7(1) - log7(sqrt(7))
= 0 -(1/2)log7(7)
= 0-1/2
= -1/2</span>
Answer:
![A = 100^o](https://tex.z-dn.net/?f=A%20%3D%20100%5Eo)
![B = 43.0^o](https://tex.z-dn.net/?f=B%20%3D%2043.0%5Eo)
![C =37.0^o](https://tex.z-dn.net/?f=C%20%3D37.0%5Eo)
Step-by-step explanation:
Given
![A = 100^o](https://tex.z-dn.net/?f=A%20%3D%20100%5Eo)
![b = 51](https://tex.z-dn.net/?f=b%20%3D%2051)
![c =45](https://tex.z-dn.net/?f=c%20%3D45)
Required
Complete the triangle (See attachment)
First, calculate side a using cosine's equation
![a^2 = b^2 + c^2 -2bc \cos A](https://tex.z-dn.net/?f=a%5E2%20%3D%20b%5E2%20%2B%20c%5E2%20-2bc%20%5Ccos%20A)
![a^2 = 51^2 + 45^2 -2*51*45 \cos (100^o)](https://tex.z-dn.net/?f=a%5E2%20%3D%2051%5E2%20%2B%2045%5E2%20-2%2A51%2A45%20%5Ccos%20%28100%5Eo%29)
![a^2 = 4626 -4590 *-0.1736](https://tex.z-dn.net/?f=a%5E2%20%3D%204626%20-4590%20%2A-0.1736)
![a^2 = 4626+ 796.8](https://tex.z-dn.net/?f=a%5E2%20%3D%204626%2B%20796.8)
![a^2 = 5422.8240](https://tex.z-dn.net/?f=a%5E2%20%3D%205422.8240)
Take square roots
![a = 73.6398](https://tex.z-dn.net/?f=a%20%3D%2073.6398)
The measure of B and C can then be calculated using sine's equation
![\frac{a}{\sin A} =\frac{b}{\sin B} =\frac{c}{\sin C}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7B%5Csin%20A%7D%20%3D%5Cfrac%7Bb%7D%7B%5Csin%20B%7D%20%3D%5Cfrac%7Bc%7D%7B%5Csin%20C%7D)
So:
![\frac{73.6398}{\sin (100)} =\frac{51}{\sin B}](https://tex.z-dn.net/?f=%5Cfrac%7B73.6398%7D%7B%5Csin%20%28100%29%7D%20%3D%5Cfrac%7B51%7D%7B%5Csin%20B%7D)
![\frac{73.6398}{0.9848} =\frac{51}{\sin B}](https://tex.z-dn.net/?f=%5Cfrac%7B73.6398%7D%7B0.9848%7D%20%3D%5Cfrac%7B51%7D%7B%5Csin%20B%7D)
Cross multiply
![\sin B * 73.6398 = 51 * 0.9848](https://tex.z-dn.net/?f=%5Csin%20B%20%2A%2073.6398%20%3D%2051%20%2A%200.9848)
![\sin B * 73.6398 = 50.2248](https://tex.z-dn.net/?f=%5Csin%20B%20%2A%2073.6398%20%3D%2050.2248)
Solve for sin B
![\sin B = \frac{50.2248}{73.6398}](https://tex.z-dn.net/?f=%5Csin%20B%20%3D%20%5Cfrac%7B50.2248%7D%7B73.6398%7D)
![\sin B = 0.6820](https://tex.z-dn.net/?f=%5Csin%20B%20%3D%200.6820)
Take arc sin of both sides
![B = \sin^{-1}(0.6820)](https://tex.z-dn.net/?f=B%20%3D%20%5Csin%5E%7B-1%7D%280.6820%29)
![B = 43.0^o](https://tex.z-dn.net/?f=B%20%3D%2043.0%5Eo)
To calculate C, we make use of:
--- angles in a triangle
![100 + 43 + C = 180](https://tex.z-dn.net/?f=100%20%2B%2043%20%2B%20C%20%3D%20180)
![143 + C = 180](https://tex.z-dn.net/?f=143%20%2B%20C%20%3D%20180)
Collect like terms
![C =180-143](https://tex.z-dn.net/?f=C%20%3D180-143)
![C =37.0^o](https://tex.z-dn.net/?f=C%20%3D37.0%5Eo)
divide 32 miles by 2 1/3 hours
32/2.33333 = 13.7143
to nearest tenth = 13.7 miles per hour