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12 days ago

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Triangle A B C is shown. Angle A C B is a right angle. The length of hypotenuse A B is 12 centimeters, the length of C B is 9.8

centimeters, and the length of A C is 6.9 centimeters. Which expressions can be used to find m∠BAC? Select three options. cos−1(StartFraction 6.9 Over 12 EndFraction) cos−1(StartFraction 9.8 Over 12 EndFraction) sin−1(StartFraction 6.9 Over 12 EndFraction) sin−1(StartFraction 9.8 Over 12 EndFraction) tan−1(StartFraction 6.9 Over 9.8 EndFraction)

2 answers:

tester [8.8K]12 days ago

6 0

Answer:

The first and fourth options are valid choices.

Step-by-step explanation:

The attached image displays the triangle mentioned in the question.

To calculate the angle BAC, we can use trigonometric relationships. Observing all sides, we can use any trigonometric function regardless.

$cos(\angle BAC)=\frac{6.9cm}{12cm} =0.575\\\angle BAC = cos^{-1} (0.575) \approx 55\°$

Thus, the first option is confirmed correct.

$sin(\angle BAC)=\frac{9.8cm}{12cm}\\\angle BAC = sin^{-1} (\frac{9.8cm}{12cm})$

The fourth option also holds true.

$tan(\angle BAC)=\frac{9.8cm}{6.9cm}\\\angle BAC = tan^{-1}(\frac{9.8cm}{6.9cm})$

The last option is incorrect since it denotes the inverse tangent function.

Inessa [9K]12 days ago

4 0

Answer:

tan−1(StartFraction 6.9 Over 9.8 EndFraction)

Step-by-step explanation:

tan−1(StartFraction 6.9 Over 9.8 EndFraction)

The tangent is defined as opposite over adjacent, thus 9.8/6.9

The inverse tangent operates as 1 / tan and equals 1 / (9.8 / 6.9) = 6.9 / 9.8

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Answer:

6.75g

Step-by-step explanation:

The initial step is to convert all values to grams using rules of three, followed by summation.

In a rule of three calculation, the first step is identifying the measures and how they interrelate; whether their connection is direct or inverse.

In direct relationships, as one measure increases, so does the other.

In inverse relationships, as one measure increases, the other decreases.

Problems involving unit conversion, like this, illustrate a direct relationship between measures.

First step: convert 0.0025kg to grams

One kilogram equals 1000 grams, so:

1kg - 1000g

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x = 1000*0.0025 = 2.5g

Thus, 0.0025kg is equal to 2.5g

Second step: handle 1750 mg

One gram consists of 1000mg, so:

1g - 1000mg

xg - 1750mg

1000x = 1750

$x = \frac{1750}{1000}$

x = 1.75g

Therefore, 1750 mg converts to 1.75g

2.25g is fine

Third step: convert 825,000 μg to grams

One gram consists of 1,000,000 micrograms, so:

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1,000,000x = 825,000

$x = \frac{825,000}{1,000,000}$

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So, 825,000 μg equals 0.25g

Final step: sum all values

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