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3 years ago

In a right triangle one leg measures a quarter of the other, how much do its acute angles measure? with procedure please

Mathematics

1 answer:

KATRIN_1 [288]3 years ago

3 0

Answer:

The answer to your question is 14° and 76°

Step-by-step explanation:

Data

leg 1 = x

leg 2 = x/4

angle 1 = ?

angle 2 = ?

Process

To solve problem use trigonometric functions. We must use the trigonometric function that relates both legs (tangent).

tangent Ф = Opposite side / Adjacent side

-Substitution

tan Ф = (x/4) / x

-Simplification

tan Ф = x / 4x

tan Ф = 1/4

- Find Ф

Ф = tan⁻¹(1/4) = 14°

- Find the other acute angle

The sum of the internal angles in a triangles equals 180°

Ф + Ф₁ + 90° = 180

-Solve for Ф₁

Ф₁ = 180 - 90 - 14

-Result

Ф₁ = 76°

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4 years ago

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<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

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The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

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The probability of a month having a PCE between $575 and $790 is the <u>p-value of Z when X = 790 subtracted by the p-value of Z when X = 575</u>, hence:

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Z = -2.5 has a p-value of 0.0062.

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More can be learned about the normal distribution at brainly.com/question/4079902

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Step-by-step explanation: