Questions: Homework Question 15, 9.3.41 Find the value of x. x= (Do not include the degree symbol in your answer. Round to the nearest degree as needed.)

Transcript text: Homework Question 15, 9.3.41 Find the value of $x$. \[ x= \] (Do not include the degree symbol in your answer. Round to the nearest degree as needed.)

Solution

Solution Steps

Step 1: Identify the given values

We are given a right triangle with hypotenuse 11 and the side opposite to angle _x_ is 5.

Step 2: Use the appropriate trigonometric ratio

We can use the sine ratio, which relates the opposite side and the hypotenuse to the angle: sin(_x_) = opposite/hypotenuse sin(_x_) = 5/11

Step 3: Solve for x

To find the value of _x_, take the inverse sine of both sides: _x_ = arcsin(5/11) _x_ ≈ 27.035

Step 4: Round to the nearest degree

Rounding to the nearest degree, we get: _x_ ≈ 27

Final Answer:

The value of x is approximately 27.

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