The two sides of the triangle are 6 cm and 12 cm and the included angle is 60°. what's the measure of the third side.
a. 6.7
b. 8.5
c. 10.4
d. 12 5

C. 10,4

Step-by-step explanation:

Using the Law of Cosines [Solving for Angle Measures → cos<A = -a² + b² + c²\2bc, cos<B = a² - b² + c²\2ac, cos<C = a² + b² - c²\2ab; Solving for Sides → a² = b² + c² - 2bc cos<A, b² = c² + a² - 2ac cos<B, c² = b² + a² - 2ab cos<C], set up your triangle with your angles and sides OPPOSITE from each other.

Suggestion: make Side b 12 and Side a 6, leaving you with Side c to find. According to the problem and how you set up your triangle, <C can be 60°. This is how you should set it up:

c² = 36 + 144 - 144 cos 60°; 108 = c²

The reason being is because 6² is 36, 12² is 144, 2ab → 2[12][6] is 144, and cos 60° is ½. Putting this altogether will give you 108 = c². Obviously, the final step is to take the square root of 108, which rounded to the nearest tenth, is 10,4.

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**Whenever you are solving for an angle using the Law of Cosines, towards your final answer, use the cos⁻¹ function to cancel the cos to isolate your angle measure.

"it's not the heat, it's the humidity".   that's a partly valid phrase you may have heard in the summer, but it's actually both.   the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature.   this has important considerations for the human body's comfort.   when the body gets too hot, it begins to perspire or sweat to cool itself off.   if the perspiration is not able to evaporate, the body cannot regulate its temperature.   evaporation is a cooling process.   when perspiration is evaporated off the body, it effectively reduces the body's temperature.   when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases.   in other words, the human body feels warmer in humid conditions.   the opposite is true when the relative humidity decreases because the rate of perspiration increases.   the body actually feels cooler in arid conditions.   there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation:

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step-by-step explanation: