Mathematics: An acute angle θ is in a right triangle with sin θ = six sevenths. what is the value of cot θ? answers 7 / (sqrt 13) (sqrt 13) / 6 6 / (sqrt 13) (sqrt 13) / 7

An acute angle θ is in a right triangle with sin θ

lindirogers19

05.01.2022

$\sin \theta =\dfrac{6}{7}\\
\cot \theta=\dfrac{x}{6}\\
x^2+6^2=7^2\\
x^2=49-36\\
x^2=13\\
x=\sqrt{13}\\
\boxed{\cot \theta =\dfrac{\sqrt{13}}{6}}$

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hlc614

05.01.2022

Consider right triangle ABC with leg BC=6, hypotenuse AB=7 and angle C such that $\sin \angle A=\dfrac{6}{7}.$

By the Pythagorean theorem, you can find the length of the second leg AC:

$AC^2+BC^2=AB^2,\\AC^2+36=49,\\AC^2=13,\\AC=\sqrt{13}.$

Use the definition of $\cot$ :

$\cot \angle A=\dfrac{\text{adjacent leg}}{\text{opposite leg}}=\dfrac{AC}{BC} =\dfrac{\sqrt{13}}{6}.$

$\cot \theta=\dfrac{\sqrt{13}}{6}.$

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mutoni55

23.11.2020

Step-by-step explanation:

Add the x values and divide by the amount of x's and same with the y's

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