Complete the proof of the Law of Sines/Cosines.

Mathematics

1 answer:

frosja888 [35]3 years ago

6 0

Answer:

(A)

Definition of altitude
c⋅sinA
$c\cdot sinA=a\cdot sinC$ .

Step-by-step explanation:

Law of Sines/Cosines.

Given triangle ABC with altitude segment BD labeled x. Angles ADB and CDB are right angles by the (1) definition of altitude making triangle ABD and triangle BCD right triangles.

Using the trigonometric ratios $sin A=\dfrac{x}{c}$ and $sin C=\dfrac{x}{a}$ .

Multiplying to isolate x in both equations gives (2) $x=c\cdot sinA$ and $x=a\cdot sinC.$

We also know that x = x by the reflexive property.

By the substitution property,(3) $c\cdot sinA=a\cdot sinC$ .

Dividing each side of the equation by ac gives:

$\frac{c\cdot sinA}{ac} =\frac{a\cdot sinC}{ac} \\\frac{ sinA}{a} =\frac{sinC}{c}$

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Systolic Blood Pressure Assume that the mean systolic blood pressure of normal adults is 120 millimeters of mercury and the stan

liq [111]

Answer:

0.1425 = 14.25% probability that the individual's pressure will be between 119.4 and 121.4mmHg.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

$\mu = 120, \sigma = 5.6$