A surveyor leaves her base camp and drives 42km on a bearing of 32 degrees. She then drives 25km on a bearing of 154 degrees. Ho
w far is she then from her base camp and what is her bearing from it
1 answer:
Answer:
35.7 km and 248.3 °
Step-by-step explanation:
To clarify, I will include a diagram as an image.
We begin with the cosine law formula:
y² = 42² + 28² - (2 * 42 * 25 * cos 58 °)
y² = 2389 - 1112.83 = 1276.17
y = √1276.17
y = 35.72 km
Next, to find the bearing of the surveyor from her camp, we apply the sine law:
[(Sin 58 °) / y] = [(Sin A) / 42]
Here, A = (42 * sin 58 °) / 35.72
A = sin⁻¹ (0.9971)
A = 85.7 °
The bearing from the base camp now calculates to: 270 ° - (85.7 ° - 64 °) = 248.3 °
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Explanation:
Step-by-step clarification:
Referring to step 6
(b² — 4ac) / 4a² = (x + b/2a)²
The mistake in the question is that it should be (x + b/2a)²
According to step 7
±√(b² —4ac) /2a = x + b/2a
The error in the question is that it should be divided by 2a, not 1a.
1. The transition from step 6 to step 7 involves taking the square roots of both sides
(b² — 4ac) / 4a² = (x + b/2a)²
Taking the square of both sides
√(b²—4ac) / √4a² = √(x + b/2a)²
√(b²—4ac) / 2a = x + b/2a
This forms step 7 correctly.
Next, subtracting b/2a from both sides
√(b²—4ac) / 2a - b/2a= x + b/2a -b/2a
√(b²—4ac) / 2a — b/2a = x
(√(b²—4ac) — b)/2a = x
x = [—b ± √(b²—4ac)] / 2a
This gives the desired formula.
The discriminant is D = b²—4ac.
