# An acute angle θ is in a right triangle with sin θ = 6/7. What is the value of cot θ?

Trigonometry is a branch of mathematics that deals with the relation between the angles and sides of a right triangle.

## Answer: In a right triangle with sin θ = 6/7, the value of cot θ = (√13) / 6.

Let's look into the stepwise solution.

**Explanation:**

Given: sin θ = 6/7

We know that for a given acute angle θ in a right triangle sin θ is expressed as:

sin θ = Opposite Side / Hypotenuse

Let's take a right-angled triangle ABC and mark the sides,

From the above diagram, we see that angle C = θ

Thus, sin θ = AB / AC [Since, AB = Opposite Side, AC = Hypotenuse]

Hence, sin θ = AB / AC = 6 / 7

We know that,

cot θ = Adjacent Side / Opposite Side = BC / AB

Thus, to calculate BC we will apply the Pythagoras theorem on triangle ABC.

According to Pythagoras theorem,

Hypotenuse^{2} = Base^{2} + Height^{2}

From triangle ABC,

⇒ AC^{2} = AB^{2} + BC^{2}

⇒ BC^{2} = AC^{2} - AB^{2}

⇒ BC^{2} = 7^{2} - 6^{2} [ Since, AC = 7, AB = 6]

⇒ BC^{2} = 49 - 36

⇒ BC^{2} = 13

⇒ BC = √13

Thus, cot θ = BC / AB = (√13) / 6

We can also use Cuemath's Online Trigonometric Ratios Calculator to calculate different trigonometric ratios.

### Hence, the value of cot θ = (√13) / 6.

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