Questions: Find the indicated side of the triangle.

Find the indicated side of the triangle.
Transcript text: Find the indicated side of the triangle.
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Solution

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Solution Steps

Step 1: Identify the given values and the required side

We are given a right triangle with:

  • One angle of 30°
  • The side opposite the 30° angle (a) is unknown
  • The side adjacent to the 30° angle (b) is unknown
  • The hypotenuse is 7
Step 2: Use the properties of a 30°-60°-90° triangle

In a 30°-60°-90° triangle:

  • The side opposite the 30° angle is half the hypotenuse.
  • The side opposite the 60° angle is the hypotenuse times √3/2.
Step 3: Calculate the side opposite the 30° angle

The side opposite the 30° angle (a) is: \[ a = \frac{1}{2} \times 7 = 3.5 \]

Step 4: Calculate the side adjacent to the 30° angle

The side adjacent to the 30° angle (b) is: \[ b = 7 \times \frac{\sqrt{3}}{2} = \frac{7\sqrt{3}}{2} \]

Final Answer

\[ b = \frac{7\sqrt{3}}{2} \]

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