Solve for x cos(52)=19/x

Problem

cos(52^∘)=19/x

Solution

1. Multiply both sides of the equation by x to move the variable out of the denominator.

x*cos(52^∘)=19

2. Divide both sides by cos(52^∘) to isolate x

x=19/cos(52^∘)

3. Evaluate the cosine of 52^∘ using a calculator.

cos(52^∘)≈0.615661

4. Calculate the final value by dividing 19 by the decimal value.

x≈30.859

Final Answer

x=19/cos(52^∘)≈30.859

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