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Nitella [24]
3 years ago
8

You need to find the distance across a river, so you make a triangle. BC is 661 feet, m∠B=103.2° and m∠C=14.4°. Find AB.

Mathematics
1 answer:
kati45 [8]3 years ago
4 0

Answer:

AB = 185.77 feet

Step-by-step explanation:

From the figure attached, in ΔABC,

m∠B = 103.2°, m∠C = 14.4° and side BC = 661 feet

We have to find the measure of side AB.

Since ∠A + ∠B + ∠C = 180°

∠A + 103.2 + 14.4 = 180

∠A + 117.6 = 180

∠A = 180 - 117.6

     = 62.4°

By applying sine rule in the given triangle ABC

\frac{AB}{sinC}=\frac{BC}{sinA}

\frac{AB}{sin14.4}=\frac{661}{sin62.4}

\frac{AB}{0.249}=\frac{661}{0.886}

AB = \frac{0.249\times661}{0.886}

     = 185.77 feet

Therefore, AB = 185.77 feet will be the answer.

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Step-by-step explanation:

a) We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

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For the alternative hypothesis,

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Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is

z = (x - µ)/(σ/√n)

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From the information given,

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Since the curve is symmetrical and it is a two tailed test, the x value for the left tail is 9 - 0.9 = 8.1

the x value for the right tail is 9 + 0.9 = 9.9

These means are higher and lower than the null mean. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area. We already got the area above the z score as z = 0.00539

We would double this area to include the area in the left tail of z = - 2.55. Thus

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But we are told to use the critical value approach, then

Since α = 0.01, the critical value is determined from the normal distribution table.

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The z score for an area to the right of 0.995 is 2.575

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(Sample mean ± margin of error)

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Margin of error = z × σ/√n

The z score for confidence level of 99% is 2.58

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