Answer to the nearest tenth. 10 30° x Not drawn to scale 17.3 8.7 5 5.8
Question 4 Use a trigonometric ratio to find the value of x. Round your answer to the nearest tenth. 10 30° x Not drawn to scale 17.3 8.7 5 5.8
The Correct Answer and Explanation is:
Answer: The correct option is 5.8.
Explanation:
To solve for the value of x, we can use trigonometric ratios. The problem provides a right-angled triangle, an angle, the length of one side, and asks for the length of another side.
1. Identify the Sides:
First, let’s identify the sides of the triangle in relation to the given angle of 30°.
- The side with length x is opposite to the 30° angle.
- The side with length 10 is adjacent to the 30° angle.
- The side opposite the right angle is the hypotenuse, which is not given a value and is not needed for this calculation.
2. Choose the Correct Trigonometric Ratio:
We need to select a trigonometric ratio that relates the opposite side and the adjacent side. The mnemonic SOH CAH TOA helps us remember the ratios:
- SOH: Sine = Opposite / Hypotenuse
- CAH: Cosine = Adjacent / Hypotenuse
- TOA: Tangent = Opposite / Adjacent
Since we have the adjacent side and need to find the opposite side, the tangent (TOA) ratio is the correct one to use.
3. Set Up and Solve the Equation:
The formula for the tangent of an angle (θ) is:
tan(θ) = Opposite / Adjacent
Substitute the known values from the triangle into this formula:
tan(30°) = x / 10
To solve for x, we can multiply both sides of the equation by 10:
x = 10 * tan(30°)
Now, we use a calculator to find the value of tan(30°):
tan(30°) ≈ 0.57735
Multiply this value by 10:
x ≈ 10 * 0.57735
x ≈ 5.7735
4. Round to the Nearest Tenth:
The problem asks to round the answer to the nearest tenth. The first digit after the decimal point is 7, and the next digit is also 7. Since the second digit is 5 or greater, we round up the first digit.
x ≈ 5.8
Therefore, the value of x is approximately 5.8.thumb_upthumb_down
