In which triangle is x equal to cos‚ÄöA¬™¬¨œÄ(4.3/6.7)?…

Mathematics Questions

In which triangle is x equal to cos‚Aª¬π(4.3/6.7)?

Short Answer

To identify triangle parameters, first determine the lengths of the adjacent side (4.3) and hypotenuse (6.7). Verify the matching triangle option and calculate the angle using the cosine function, defined as Cos x = Adjacent/Hypotenuse, leading to x = cos^{-1}(4.3/6.7).

Step-by-Step Solution

Step 1: Identify Triangle Parameters

Start by identifying the key dimensions of the triangle. In this case, we need to focus on the adjacent side and the hypotenuse. For our specific triangle, these values are:

  • Adjacent side = 4.3
  • Hypotenuse = 6.7

Step 2: Recognize the Correct Triangle Option

Next, we will look through given options to find which triangle matches our previously identified parameters. After evaluating the options:

  • Option A is determined to align with both the adjacent side of 4.3 and the hypotenuse of 6.7.

Step 3: Verify Using Trigonometric Functions

Finally, we will use the SOH CAH TOA trigonometric identity to verify our findings. According to this identity:

  • “Cosine” (Cos) relates the adjacent side to the hypotenuse.
  • Use the formula: Cos x = Adjacent/Hypotenuse which gives Cos x = 4.3/6.7.
  • To find the angle, calculate x = cos^{-1}(4.3/6.7).

Related Concepts

Key Dimensions

The specific measurements or lengths that define the size and shape of a triangle, particularly those needed for calculations like the adjacent side and hypotenuse

Adjacent Side

The side of a right triangle that is next to the angle of interest and does not include the hypotenuse

Hypotenuse

The longest side of a right triangle, opposite the right angle, which is used in trigonometric calculations.

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