Questions: Find x. (reminder: angles-whole number; sides-1 decimal place)

Transcript text: Find $x$. (reminder: angles-whole \#; sides-1 decimal place)

Solution

Solution Steps

Step 1: Find the third angle

The sum of the angles in a triangle is 180°. Therefore, the third angle is 180° - 75° - 47° = 58°.

Step 2: Use the Law of Sines

We can use the Law of Sines to find _x_. The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is the same for all three sides of a triangle. In this case, we have:

x / sin(47°) = 52 / sin(75°)

Step 3: Solve for x

Multiplying both sides by sin(47°), we get:

x = 52 * sin(47°) / sin(75°)

x ≈ 52 * 0.731 / 0.966

x ≈ 39.048

Final Answer

x ≈ 39.0

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