In triangle GHI, if angle G = 30° and angle H = 60°, what is the length of side

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Question: In triangle GHI, if angle G = 30° and angle H = 60°, what is the length of side g opposite angle G if side h opposite angle H is 10 units?

Options:

5
8.66
10
12

Correct Answer: 8.66

Solution:

Using the sine rule: g/h = sin(G)/sin(H) => g/10 = sin(30°)/sin(60°) => g = 10 * (1/2) / (√3/2) = 10/√3 = 8.66.

In triangle GHI, if angle G = 30° and angle H = 60°, what is the length of side

Practice Questions

In triangle GHI, if angle G = 30° and angle H = 60°, what is the length of side g opposite angle G if side h opposite angle H is 10 units?

5
8.66
10
12

Questions & Step-by-Step Solutions

In triangle GHI, if angle G = 30° and angle H = 60°, what is the length of side g opposite angle G if side h opposite angle H is 10 units?

Step 1: Identify the angles in triangle GHI. We have angle G = 30° and angle H = 60°.
Step 2: Recognize that side g is opposite angle G and side h is opposite angle H. We know side h = 10 units.
Step 3: Use the sine rule, which states that the ratio of a side length to the sine of its opposite angle is the same for all sides in a triangle. The formula is g/h = sin(G)/sin(H).
Step 4: Substitute the known values into the sine rule: g/10 = sin(30°)/sin(60°).
Step 5: Calculate sin(30°) and sin(60°). We know sin(30°) = 1/2 and sin(60°) = √3/2.
Step 6: Substitute these values into the equation: g/10 = (1/2) / (√3/2).
Step 7: Simplify the right side: g/10 = (1/2) * (2/√3) = 1/√3.
Step 8: Multiply both sides by 10 to solve for g: g = 10 * (1/√3).
Step 9: Calculate the value: g = 10/√3, which is approximately 8.66.

Sine Rule – The sine rule relates the lengths of sides of a triangle to the sines of its angles, allowing for the calculation of unknown side lengths when certain angles and side lengths are known.
Triangle Angle Sum – The sum of the angles in a triangle is always 180°, which can help verify the angles given in the problem.

In triangle GHI, if angle G = 30° and angle H = 60°, what is the length of side

What’s inside this PDF?

In triangle GHI, if angle G = 30° and angle H = 60°, what is the length of side

Practice Questions

Questions & Step-by-Step Solutions

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