Questions: Find x. (reminder: angles-whole #; sides-1 * 2 points decimal place)

Find x. (reminder: angles-whole #; sides-1 * 2 points decimal place)
Transcript text: Find x. (reminder: angles-whole \#; sides-1 * 2 points decimal place)
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Solution

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Solution Steps

Step 1: Find the third angle of the triangle

The sum of the angles in a triangle is 180°. We have two angles, 35° and 112°. The third angle is 180° - 35° - 112° = 33°.

Step 2: Use the Law of Sines

The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides and angles in a triangle. In our case:

x / sin(35°) = 45 / sin(112°)

Step 3: Solve for x

x = 45 * sin(35°) / sin(112°) x ≈ 45 * 0.5736 / 0.9272 x ≈ 27.7

Final Answer

The value of x is approximately 27.7.

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