Answer:
A. Yes,
B. An underestimate could lead to you being stranded on a road trip in the middle of nowhere without guess. When it comes to these things, it's better to have more than necessary. After all, you'd rather have gas and not need it than need it and not have it.
Step-by-step explanation:
A. We can quickly calculate that 12 x 30 = 360. We need to travel 10 more miles to get to 370, but we have 2 miles per gallon and 12 gallons of gas, or 12 x 2 = 24 more miles! Upon further inspection it is evident that 12 x 32 = 360 + 24 = 384 which is indeed larger than 370.
B. Answer contains explanation.
Check the picture below.
what's the width? well, w = (2/3)l.
Answer:
Step-by-step explanation:
Answer:
- q = 9.2
- P = 45.6°
- R = 79.4°
Step-by-step explanation:
The two given sides are either side of the given angle. This provides insufficient information for using the Law of Sines, which needs an angle and a side opposite. However, it is exactly what is needed to make use of the Law of Cosines.
Thus, the Law of Cosines can be used to find side length q.
q² = p² +r² -2pr·cos(Q)
q² = 8² +11² -2·8·11·cos(55°) ≈ 64 +121 -100.949 ≈ 84.051
q ≈ √(84.051) ≈ 9.1679 ≈ 9.2
Then the Law of Sines can be used to find angle P. We choose to find the smaller angle in order to avoid the ambiguity that can come with trying to determine if the larger angle is acute or obtuse.
sin(R)/r = sin(Q)/q
P = arcsin(p/q·sin(Q)) ≈ arcsin(8/9.1679·sin(55°)) ≈ 45.627° ≈ 45.6°
R = 180° -Q -P = 180° -55° -45.6° = 79.4°
__
The solution is ...
q = 9.2
∠P = 45.6°
∠R = 79.4°