In triangle GHI, if angle G = 50 degrees and angle H = 70 degrees, what is the l

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Question: In triangle GHI, if angle G = 50 degrees and angle H = 70 degrees, what is the length of side GH if side GI = 10 cm?

Options:

Correct Answer: 10 cm

Solution:

Using the Law of Sines, GH / sin(I) = GI / sin(G). Since angles sum to 180, angle I = 60 degrees. Thus, GH = 10 * sin(60) / sin(50).

In triangle GHI, if angle G = 50 degrees and angle H = 70 degrees, what is the length of side GH if side GI = 10 cm?

In triangle GHI, if angle G = 50 degrees and angle H = 70 degrees, what is the length of side GH if side GI = 10 cm?

Step 1: Identify the angles in triangle GHI. We know angle G = 50 degrees and angle H = 70 degrees.
Step 2: Calculate angle I using the fact that the sum of angles in a triangle is 180 degrees. So, angle I = 180 - (angle G + angle H) = 180 - (50 + 70) = 60 degrees.
Step 3: Write down the Law of Sines formula: GH / sin(I) = GI / sin(G).
Step 4: Substitute the known values into the formula: GH / sin(60) = 10 / sin(50).
Step 5: Rearrange the formula to solve for GH: GH = 10 * sin(60) / sin(50).
Step 6: Calculate the values of sin(60) and sin(50) using a calculator or trigonometric tables.
Step 7: Substitute the values of sin(60) and sin(50) into the equation to find GH.

Law of Sines – A mathematical formula used to relate the lengths of sides of a triangle to the sines of its angles.
Triangle Angle Sum – The principle that the sum of the angles in a triangle is always 180 degrees.