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Let a, b, and c be the measures of three angles of a triangle. It is known that: 51.3°≤a≤51.5° and 72.9°≤b≤73.3°. What are all possible values of c?

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TaeKwonDoIsDead

Answer:

55.2° ≤ c ≤ 55.8°

Step-by-step explanation:

We know a + b + c = 180

Let's take the smallest value of a and b and find largest value of c:

51.3 + 72.9 + c = 180

c = 55.8

Now,

Let's take the largest value of a and b and find smallest value of c:

51.5 + 73.3 + c = 180

c = 55.2

Thus, we can say, range of c is:

55.2° ≤ c ≤ 55.8°

  • The sum of angles in a triangle = 180°

  • It is known that: 51.3°≤a≤51.5° and 72.9°≤b≤73.3°

  • Step 1: The first possible value of c is calculated as :

Adding the biggest value of a and b together and subtracting it from 180°

Biggest value of a = 51.5°

Biggest value of b = 73.3°

Hence, 51.5° + 73.3° + c = 180°

124.8° +  c = 180°

c = 180° - 124.8°

c = 55.2°

  • Step 2: The second possible value of c is calculated as :

Adding the least value of a and b together and subtracting it from 180°

Least value of a = 51.3°

Least value of b = 72.9°

Hence, 51.3° + 72.9° + c = 180°

124.2° +  c = 180°

c = 180° - 124.2°

c = 55.8°

Therefore, all the possible values of " c "are 55.2° and 55.8°

To learn more, please visit the link below:

https://brainly.com/question/21741558

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