In triangle STU, if angle S = 30 degrees and angle T = 70 degrees, what is the l

₹0.0

Question: In triangle STU, if angle S = 30 degrees and angle T = 70 degrees, what is the length of side SU if ST = 10 cm and TU = 15 cm?

Options:

Correct Answer: 12.5 cm

Solution:

Using the Law of Sines: SU / sin(80) = 10 / sin(30). Therefore, SU = 10 * sin(80) / sin(30) = 10 * 0.9848 / 0.5 = 19.696 cm.

In triangle STU, if angle S = 30 degrees and angle T = 70 degrees, what is the length of side SU if ST = 10 cm and TU = 15 cm?

In triangle STU, if angle S = 30 degrees and angle T = 70 degrees, what is the length of side SU if ST = 10 cm and TU = 15 cm?

Step 1: Identify the angles in triangle STU. We know angle S = 30 degrees and angle T = 70 degrees.
Step 2: Calculate angle U using the fact that the sum of angles in a triangle is 180 degrees. So, angle U = 180 - (30 + 70) = 80 degrees.
Step 3: Write down the lengths of the sides we know: ST = 10 cm and TU = 15 cm.
Step 4: Use the Law of Sines, which states that the ratio of a side length to the sine of its opposite angle is the same for all three sides. We want to find side SU.
Step 5: Set up the equation using the Law of Sines: SU / sin(80) = ST / sin(30). This means SU / sin(80) = 10 / sin(30).
Step 6: Rearrange the equation to solve for SU: SU = 10 * sin(80) / sin(30).
Step 7: Calculate sin(80) and sin(30). We know sin(30) = 0.5 and sin(80) is approximately 0.9848.
Step 8: Substitute the values into the equation: SU = 10 * 0.9848 / 0.5.
Step 9: Perform the calculation: SU = 10 * 0.9848 = 9.848, then divide by 0.5 to get SU = 19.696 cm.

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