Questions: Find the value of each trigon 1) tan Z

Find the value of each trigon 1) tan Z
Transcript text: Find the value of each trigon 1) $\tan Z$
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Solution

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Solution Steps

Step 1: Identify the sides of the triangle

In the given right triangle, we have:

  • Opposite side to angle Z: XY = 21
  • Adjacent side to angle Z: ZY = 28
  • Hypotenuse: XZ = 35
Step 2: Recall the definition of tangent

The tangent of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side.

Step 3: Calculate tan Z

Using the definition of tangent: \[ \tan Z = \frac{\text{opposite}}{\text{adjacent}} = \frac{XY}{ZY} = \frac{21}{28} \]

Step 4: Simplify the fraction

Simplify \(\frac{21}{28}\): \[ \frac{21}{28} = \frac{3}{4} \]

Final Answer

\[ \tan Z = \frac{3}{4} \]

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