Questions: Calculate sin θ if a=5 and c=6.

Calculate sin θ if a=5 and c=6.
Transcript text: Calculate $\sin \theta$ if $a=5$ and $c=6$.
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Solution

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Solution Steps

Step 1: Find the length of the opposite side

We are given a right triangle with adjacent side _a_ = 5 and hypotenuse _c_ = 6. We need to find the length of the opposite side _b_. We can use the Pythagorean theorem: _a_² + _b_² = _c_². Substituting the given values, we have: 5² + _b_² = 6² 25 + _b_² = 36 _b_² = 36 - 25 _b_² = 11 _b_ = √11

Step 2: Calculate sin θ

sin θ = opposite/hypotenuse = _b_/ _c_ = √11 / 6

Final Answer:

√11 / 6

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