Final answer:
To find the value of x using a trigonometric ratio, identify known sides or angles, select an appropriate trigonometric ratio, set up and solve the equation, then round the answer to the nearest tenth and check if it's reasonable.
Step-by-step explanation:
To use a trigonometric ratio to find the value of x, we need to know the specific trigonometric relationship provided in the question and the given angle or side lengths. A common formula used is TL = TLX / cos(θ), where TL is the length of the side adjacent to the angle, TLX is the hypotenuse, and θ (theta) is the angle. It is also important to remember that angles should be measured in radians when performing trigonometric calculations.
Here's a general step-by-step guide to similar problems:
- Identify the known sides or angles of the triangle.
- Select an appropriate trigonometric ratio (sine, cosine, or tangent) depending on the known and unknown sides.
- Set up the equation using the selected trigonometric ratio.
- Substitute the known values into the equation.
- Solve for the unknown variable, x.
- Round your answer to the nearest tenth as instructed.
- Perform a reasonability check to ensure your answer makes sense.
Example:
If you have a right triangle with an adjacent side length of 3 cm and an angle of 60 degrees, and you need to find the hypotenuse (x), you would use the cosine ratio:
cos(60°) = 3 cm / x
x = 3 cm / cos(60°)
Then calculate the value of x using a calculator and round to the nearest tenth.
Always ensure units are consistent and that your final answer is reasonable given the context of the problem.