Answer :
Final answer:
The length of TV in triangle TUV is approximately 236 cm
The correct answer is C) 236 cm.
Explanation:
To find the length of TV in triangle TUV, we can use the Law of Cosines since we have one angle and two sides given.
Given:
U = 750 cm
V = 670 cm
∠T = 160°
Using the Law of Cosines:
TV² = TU² + UV² - 2(TU)(UV)cos(T)
Substitute the given values:
TV² = 750² + 670² - 2(750)(670)cos(160°)
Calculate the value of TV:
TV ≈ 236 cm (rounded to the nearest centimeter)
Therefore, the length of TV is approximately 236 cm, which corresponds to option c) 236 cm.
To find the length of TV in a triangle with specific measurements, use the cosine rule and calculation to determine the nearest centimeter length, which in this case is 315 cm (option a).
Given: U = 750 cm, V = 670 cm, and ∠T = 160°
To find: The length of TV, to the nearest centimeter
Solution:
- Use the cosine rule: TV² = TU² + UV² - 2(TU)(TV)cos(∠T)
- Substitute the given values and calculate to find TV
- Round the result to the nearest centimeter o find the length of TV in riangle TUV where U = 750 cm, V = 670 cm, and \∠T = 160°, we can use the Law of Cosines. The Law of Cosines states that for a triangle with sides a, b, and c, and the angle opposite side c being γ, c² = a² + b² - 2ab \cos(γ).
- In this case, the side lengths 'a' and 'b' are given as U = 750 cm and V = 670 cm, and the angle 'γ' is \∠T = 160°. Plugging these values into the formula:
- TV² = U² + V² - 2 * U * V * \cos(∠T) = 750² + 670² - 2 * 750 * 670 * \cos(160°)
- Calculating the above expression gives us the square of the length of TV,
- TV = \sqrt(TV²)
- After calculating TV² and taking the square root, round the result to the nearest centimeter to find the correct length of TV among the options provided.
The correct answer is 315 cm (option a).