Question

Find the length of GI in the triangle below. Show your work.

Answer 1

Answer:

the length of GI in the triangle is 90 approximately

Step-by-step explanation:

To find the length GI in the triangle below, since two sides of the triangle is given and only one angle is given, the best formula to use is the cosine  formula;

h² = g² + i² - 2gi cos H

GI = h = ?

GH = i = 60

HI = g = 42

H= 123°

We can now proceed to insert our values into the formula;

h² = g² + i² - 2gi cos H

h² = 42² + 60² - 2(42)(60) cos 123

   =1764 + 3600 -  5040 (-0.5446)

   =5364 + 2744.784

   = 8108.784

h² = 8108.784

Take the square root of both-side

√h² = √8108.784

h =90.049

h≈90

Therefore, the length of GI in the triangle is 90 approximately.

Answer 2

Answer:

The length of GI is 90.06 units

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

GH = 60 units

HI = 42 units

∠H = 123°

2. Using the Law of Cosines, we can find the length of GI, this way:

GI² = GH² + HI² - 2 * GH * HI * cos ∠H

Replacing with the real values:

GI² = 60² + 42² - 2 * 60 * 42 * cos ∠123°

GI² = 3,600 + 1,764 - 2 * 60 * 42 * -0.545

GI² = 3,600 + 1,764 - 2 * 60 * 42 * -0.545

GI² = 3,600 + 1,764 + 2,746.8

GI² = 8,110.8

GI = √ 8,110.8 = 90.06 units