Answer:
7.9km
Step-by-step explanation:
(a)See attached for the diagram representing this situation.
(b)
In Triangle ABC
![\text{Using Law of Sines}\\\dfrac{\sin A}{a}=\dfrac{\sin C}{c} \\\dfrac{\sin A}{5.2}=\dfrac{\sin 58^\circ}{6.8} \\\sin A=5.2 \times \dfrac{\sin 58^\circ}{6.8}\\A=\arcsin (5.2 \times \dfrac{\sin 58^\circ}{6.8})\\A=40.43^\circ](https://tex.z-dn.net/?f=%5Ctext%7BUsing%20Law%20of%20Sines%7D%5C%5C%5Cdfrac%7B%5Csin%20A%7D%7Ba%7D%3D%5Cdfrac%7B%5Csin%20C%7D%7Bc%7D%20%5C%5C%5Cdfrac%7B%5Csin%20A%7D%7B5.2%7D%3D%5Cdfrac%7B%5Csin%2058%5E%5Ccirc%7D%7B6.8%7D%20%5C%5C%5Csin%20A%3D5.2%20%5Ctimes%20%5Cdfrac%7B%5Csin%2058%5E%5Ccirc%7D%7B6.8%7D%5C%5CA%3D%5Carcsin%20%285.2%20%5Ctimes%20%5Cdfrac%7B%5Csin%2058%5E%5Ccirc%7D%7B6.8%7D%29%5C%5CA%3D40.43%5E%5Ccirc)
Next, we determine the value of Angle B.
![\angle A+\angle B+\angle C=180^\circ\\40.43+58+\angle B=180^\circ\\\angle B=180^\circ-(40.43+58)\\\angle B=81.57^\circ](https://tex.z-dn.net/?f=%5Cangle%20A%2B%5Cangle%20B%2B%5Cangle%20C%3D180%5E%5Ccirc%5C%5C40.43%2B58%2B%5Cangle%20B%3D180%5E%5Ccirc%5C%5C%5Cangle%20B%3D180%5E%5Ccirc-%2840.43%2B58%29%5C%5C%5Cangle%20B%3D81.57%5E%5Ccirc)
Finally, we find b.
![\text{Using Law of SInes}\\\dfrac{b}{\sin B}=\dfrac{c}{\sin C} \\\dfrac{b}{\sin 81.57^\circ}=\dfrac{6.8}{\sin 58^\circ} \\b=\dfrac{6.8}{\sin 58^\circ} \times \sin 81.57^\circ\\b=7.9km $ (to the nearest tenth of a kilometer)](https://tex.z-dn.net/?f=%5Ctext%7BUsing%20Law%20of%20SInes%7D%5C%5C%5Cdfrac%7Bb%7D%7B%5Csin%20B%7D%3D%5Cdfrac%7Bc%7D%7B%5Csin%20C%7D%20%5C%5C%5Cdfrac%7Bb%7D%7B%5Csin%2081.57%5E%5Ccirc%7D%3D%5Cdfrac%7B6.8%7D%7B%5Csin%2058%5E%5Ccirc%7D%20%5C%5Cb%3D%5Cdfrac%7B6.8%7D%7B%5Csin%2058%5E%5Ccirc%7D%20%5Ctimes%20%5Csin%2081.57%5E%5Ccirc%5C%5Cb%3D7.9km%20%24%20%28to%20the%20nearest%20tenth%20of%20a%20kilometer%29)
The distance between the small plane and the observation tower is 7.9km.
Step-by-step explanation:
The mountain bike goes back down the hill to get his water bottle
Answer:
Step-by-step explanation:
(2n+ 2)(6n+ 1)
2n+6n=8n
1+2=3
=8n+3
Answer:
The answer is 25.5.
Step-by-step explanation:
30% of $85 is 25.5.
Answer:
B
Step-by-step explanation:
The cube of twice a number =
![{2m}^{3}](https://tex.z-dn.net/?f=%7B2m%7D%5E%7B3%7D)
Decreased by 11 =
![- 11](https://tex.z-dn.net/?f=%20-%2011)
Hence, the cube of twice a number decreased by 11 =
![{2m}^{3} - 11](https://tex.z-dn.net/?f=%20%7B2m%7D%5E%7B3%7D%20%20-%2011)