Math Problem Statement

What is the value of the missing side of this triangle? (round to the nearest tenth place). The triangle has a given angle of 26°, an adjacent side of 17 units, and the opposite side labeled as x.

Solution

To solve for xx, the missing side of the triangle, we apply trigonometry. Here's the reasoning:

Step 1: Identify given information

  • The triangle involves the given side 1717, which is adjacent to the angle 2626^\circ.
  • The unknown side xx is opposite to the angle 2626^\circ.
  • The trigonometric function that relates the opposite and adjacent sides is the tangent function: tan(angle)=oppositeadjacent\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}

Step 2: Write the tangent equation

tan(26)=x17\tan(26^\circ) = \frac{x}{17}

Step 3: Solve for xx

Rearrange the equation to isolate xx: x=17tan(26)x = 17 \cdot \tan(26^\circ)

Step 4: Calculate the value

Using a calculator: tan(26)0.4877\tan(26^\circ) \approx 0.4877 x=170.48778.3x = 17 \cdot 0.4877 \approx 8.3

Final Answer:

The value of xx, rounded to the nearest tenth, is: 8.3\boxed{8.3}


Would you like a detailed explanation of any specific step or concept?

5 Related Questions:

  1. How do we choose which trigonometric function to use in different triangle problems?
  2. What other ways can we solve for xx if additional sides or angles were provided?
  3. Can this triangle be solved using the Pythagorean theorem?
  4. How is the tangent function derived in trigonometry?
  5. What are some practical applications of this problem-solving approach?

Tip:

Always double-check whether your calculator is in degree mode when working with angles given in degrees.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Tangent Function
Solving Right Triangles

Formulas

tan(angle) = opposite/adjacent
x = adjacent * tan(angle)

Theorems

Trigonometric Functions in Right Triangles

Suitable Grade Level

Grades 9-12