Questions: Trigonometric ratios: find a side length Find ST. Write your answer as an integer or as a dec ST=

Trigonometric ratios: find a side length Find ST. Write your answer as an integer or as a dec ST=
Transcript text: Trigonometric ratios: find a side length Find ST. Write your answer as an integer or as a dec \[ S T= \]
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Solution

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Solution Steps

Step 1: Identify the given information

We are given a right triangle STR with angle S = 58° and side RT = 6.5. We are asked to find the length of ST.

Step 2: Use trigonometric ratios

Since we have a right triangle, we can use trigonometric ratios. We are given the angle S and the side adjacent to it (RT), and we want to find the side opposite to it (ST). The tangent function relates these:

tan(S) = opposite/adjacent = ST/RT

Step 3: Solve for ST

Substitute the given values:

tan(58°) = ST/6.5

ST = 6.5 * tan(58°)

ST ≈ 6.5 * 1.6003

ST ≈ 10.402

Final Answer

The length of ST is approximately 10.4

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