Question

solve for ( x ). round to the nearest tenth, if necessary.
answer attempt 3 out of 8
( x = )
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Explanation:

Step1: Identify the trigonometric ratio

In right triangle \( \triangle NOP \), \( \angle O = 90^\circ \), \( \angle P = 23^\circ \), and the side adjacent to \( \angle P \) is \( OP = 36 \), and the hypotenuse is \( NP = x \). We use the cosine function, which is defined as \( \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}} \). So, \( \cos(23^\circ)=\frac{OP}{NP}=\frac{36}{x} \).

Step2: Solve for \( x \)

From \( \cos(23^\circ)=\frac{36}{x} \), we can rearrange the formula to solve for \( x \). Multiply both sides by \( x \): \( x\cos(23^\circ)=36 \). Then divide both sides by \( \cos(23^\circ) \): \( x = \frac{36}{\cos(23^\circ)} \).

Step3: Calculate the value

We know that \( \cos(23^\circ)\approx0.9205 \). Substitute this value into the formula: \( x=\frac{36}{0.9205}\approx39.1 \).

Answer:

\( x \approx 39.1 \)