Math Problem Statement

Solve for x is it -10, 6, 10, -6

Solution

To solve for xx using the given options, let's re-evaluate the problem and consider the correct usage of trigonometric functions in this context:

  1. Identify the right triangle properties:

    • One angle is 6464^\circ, another is 2727^\circ, and the third angle is 9090^\circ.
    • The side adjacent to the 2727^\circ angle is 97+x97 + x.
    • The side opposite the 2727^\circ angle is the vertical side.
  2. Using trigonometric relationships: Since we have the opposite and adjacent sides for angle 2727^\circ: tan(27)=oppositeadjacent\tan(27^\circ) = \frac{\text{opposite}}{\text{adjacent}}

  3. Given tan(27)0.5095\tan(27^\circ) \approx 0.5095: tan(27)=97+xx\tan(27^\circ) = \frac{97 + x}{x} 0.5095=97+xx0.5095 = \frac{97 + x}{x}

  4. Solve for xx: 0.5095x=97+x0.5095x = 97 + x 0.5095xx=970.5095x - x = 97 0.4905x=97-0.4905x = 97 x=970.4905x = \frac{97}{-0.4905} x197.77x \approx -197.77

Since the options provided are -10, 6, 10, and -6, let's use each to see which one fits:

  1. Option x=10x = -10: 0.5095=9710100.5095 = \frac{97 - 10}{-10} 0.509587100.50958.70.5095 \neq \frac{87}{-10} \Rightarrow 0.5095 \neq -8.7

  2. Option x=6x = 6: 0.5095=97+660.5095 = \frac{97 + 6}{6} 0.5095=10360.509517.170.5095 = \frac{103}{6} \Rightarrow 0.5095 \neq 17.17

  3. Option x=10x = 10: 0.5095=97+10100.5095 = \frac{97 + 10}{10} 0.5095=107100.509510.70.5095 = \frac{107}{10} \Rightarrow 0.5095 \neq 10.7

  4. Option x=6x = -6: 0.5095=97660.5095 = \frac{97 - 6}{-6} 0.5095=9160.509515.170.5095 = \frac{91}{-6} \Rightarrow 0.5095 \neq -15.17

Thus, none of the provided options (-10, 6, 10, -6) correctly satisfies the equation. There may be a need to re-evaluate the triangle setup or the problem's context.

Would you like more details, or do you have any questions? Here are 5 questions you might ask:

  1. How can I verify the accuracy of my trigonometric calculations?
  2. What are some common mistakes to avoid in trigonometry problems?
  3. Can you provide a different method to solve this problem?
  4. How do the given options affect the final solution?
  5. Can you provide another example of solving a right triangle with different given sides?

Tip: Always double-check your trigonometric relationships and ensure your setup aligns with the given problem.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Right triangle properties
Trigonometric functions

Formulas

Trigonometric ratio: tan(θ) = opposite/adjacent

Theorems

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Suitable Grade Level

High School