So for this, we will be applying the Triangle Inequality Theorem, which states that the sum of 2 sides must be greater than the third side for it to be a triangle. If any inequality turns out to be false, then the set cannot be a triangle.
Let A = 6, B = 10, and C = 12:
Let A = 5, B = 7, and C = 10
Let A = 4, B = 4, and C = 9
Let A = 2, B = 3, and C = 3
Since the third option had an inequality that was false, <u>the third option cannot be a triangle.</u>
Answer:
41°
Step-by-step explanation:
This problem involving the Law of Cosines has been mostly worked for you. The value of the cosine is the solution to the remaining one-step linear equation. The inverse cosine function (cos⁻¹ or arccos) is used to find the angle from the value of the cosine.
-1125 = -1500·cos(A)
cos(A) = -1125/-1500 = 3/4 . . . . . divide by -1500 (this is the one step)
A = arccos(3/4) ≈ 41.4096°
The angle formed by the lines to the lampposts is about 41°.
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<em>Additional comment</em>
If you find the angle using the ACOS( ) function of a spreadsheet, you will always get the result in radians. Most calculators offer the choice of units for angles, so be sure you set the mode appropriately.
In the calculator screenshot, there is a decimal point in the fraction to force the angle result to be displayed as a numerical value. Otherwise, this calculator shows cos⁻¹(3/4), which isn't terribly helpful.
The line GH bisects The triangle FGI meaning it divides it into two equal parts <em>(that is the definition if bisection); </em>therefore, the angles FGH and HGI are equal:
Now let us add 2 to both sides gives
subtracting 4x from both sides gives
Hence, x = 11.
The measure of FGH is
(B)
The measure of HGI is
(C)
The measure of FGI is the sum of HGI and FGH:
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