Mathematics, 02.09.2019 14:30 kruzyoungblood8

Imagine you are responsible for writing an advice column about mathematics. the following question is submitted to your column: dear math guru, i am in trouble! i was asked to find the area of a triangle but all i know is that the longest side of the triangle is 13 units, the shortest side is 7 units, the third side is 8 units, and two of the angle measures are 32° and 28°. what do i do? how should you respond? as a group, come up with an explanation that will the student. you may wish to draw some figures of your own and describe them to the class. be sure you address the problem for the student and provide accurate and detailed information. work together to determine the best answer for the student.

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Answer from: gummybear1398

Explanation:

There are two different formulas that are useful with the given information:

Area = (1/2)ab·sin(C)

Area = √(s(s-a)(s-b)(s-c)) . . . where s=(a+b+c)/2

It does not matter which sides are designated a, b, and c. Angle C will be opposite side c.

The third angle can be computed based on the fact that the sum of angles in a triangle is 180°. It will be 180° -32° -28° = 120°. The least-to-greatest order of the angles is the same as the least-to-greatest order of the length of the opposite side. So, we might have ...

a = 7, A = 28°b = 8, B = 32°c = 13, C = 120°

Utilizing the first formula, the area is ...

Area = (1/2)(7)(8)sin(120°) = 14√3 ≈ 24.249 . . . square units

Utilizing the second formula, the area is ...

s = (7+8+13)/2 = 14

Area = √(14(14-7)(14-8)(14-13)) = 14√3 ≈ 24.249 . . . square units

For the answer to be complete, it should be noted that using either of the other two angles will give different results for the area. That is because those angles are not exact values, but are rounded to the nearest degree. Using the first formula with the different angles, we get ...

area = (1/2)(8)(13)sin(28°) ≈ 24.413 . . . square unitsarea = (1/2)(7)(13)sin(32°) ≈ 24.111 . . . square units

The first of these answers is a little high because 28° is a little more than the actual value of the angle. Likewise, the second of these answers is a little low because 32° is slightly smaller than the actual angle.

In short, the most accurate information available should be used if the answer is to be the most accurate possible. If the angles are exact, then their values should be used. If the side measures are exact, then their values should be used. In general, it will be easier to make accurate measurements of the side lengths than to make accurate angle measurements.

Imagine you are responsible for writing an advice column about mathematics. the following question i

Answer from: Quest

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step-by-step explanation:

Answer from: Quest

Okay so for every triangle has three angles that always add up to 180 degrees. and to tell the difference between whether they are secure, right or obtuse is that acute: has one angle that is less than 90 degrees. right triangle means there is at least one angle that is exactly 90 degrees. and an obtuse angle has an angle that is bigger than 180 degrees. i’ll do #13 as an example: 13. 40 and 50 so if every triangle has 180 degrees 40+50= 90 degrees then180-90= 90 degrees so the third angle is 90 degrees and because this triangle has a 90 degree angle it means it is a right triangle

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