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elena-14-01-66 [18.8K]
3 years ago
13

Find the distance between the two points rounding to the nearest tenth (if necessary).

Mathematics
1 answer:
Ket [755]3 years ago
6 0

Answer:

2.8 units

Step-by-step explanation:

d =  \sqrt{ {(3 - 1)}^{2}  +  {(6 - 8)}^{2} }  \\  \\ d =  \sqrt{ {(2)}^{2}  +  {( - 2)}^{2} }  \\  \\ d =  \sqrt{4 + 4} \\  \\ d =  \sqrt{8}  \\  \\ d = 2.82842712 \\  \\ d  \approx \: 2.8 \: units

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The equation  x=tan^{-1}(\frac{12}{5}) can be used to find the measure of ∠BAC ⇒ 2nd answer

Step-by-step explanation:

Let us revise the trigonometry ratios in the right triangle ABC, where B is the right angle, AC is the hypotenuse, AB and BC are the legs of the triangle

The trigonometry ratios of the ∠BAC, the opposite side to this angle is BC and the adjacent side to it is AB are

  • sin(BAC)=\frac{opposite}{hypotenuse}=\frac{BC}{AC}
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In Δ ABC

∵ ∠ BCA is a right angle

∴ The hypotenuse is AB

∵ The adjacent side to ∠CAB is AC

∵ The opposite side to ∠CAB is BC

∵ AB = 13 units ⇒ hypotenuse

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∵ AC = 5 units ⇒ adjacent

- Let us find the trigonometry ratios of angle BAC

∵ m∠CAB is x

∵ sin(x)=\frac{BC}{AB}

∴ sin(x)=\frac{12}{13}

∴ x=sin^{-1}(\frac{12}{13})

∵ cos(x)=\frac{AC}{AB}

∴ cos(x)=\frac{5}{13}

∴ x=cos^{-1}(\frac{5}{13})

∵ tan(x)=\frac{BC}{AC}

∴ tan(x)=\frac{12}{5}

∴ x=tan^{-1}(\frac{12}{5})

The equation  x=tan^{-1}(\frac{12}{5}) can be used to find the measure of ∠BAC

Learn more:

You can learn more about the trigonometry ratios in brainly.com/question/4924817

#LearnwithBrainly

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