Triangle Trigonometry Worksheets Grade 11

1. Isabella is a marine archaeologist mapping a triangular underwater site. She measures two sides of the site as 18 meters and 25 meters, and the angle opposite the 18-meter side is 32°. She needs to determine whether this information defines one unique triangle, two possible triangles, or no triangle at all to plan her excavation grid. How many distinct triangles are possible with these measurements?
2. Emma is a marine biologist measuring the distance between two buoys in a triangular research zone. She knows that one side of the triangle between buoy A and buoy B is 40 meters, the side between buoy A and buoy C is 55 meters, and the angle at buoy A between these two sides is 45°. Emma needs to calculate the exact distance between buoy B and buoy C to plan her boat route. What is the distance between buoy B and buoy C?
3. sin(π/4)cos(π/4) + cos(π/4)sin(π/4) = ?

…and 4 more problems

1. sin(π/3)cos(π/6) + cos(π/3)sin(π/6) = ?
2. A triangle has sides of length 9 and 12 with an included angle of 60°. Find the length of the third side.
3. sin(3π/4)cos(π/4) + cos(3π/4)sin(π/4) = ?

…and 4 more problems

1. A right triangle is positioned on a coordinate plane with vertices at (0,0), (6,0), and (6,8). A circle is circumscribed around this triangle. What are the coordinates of the center of this circumscribed circle?
2. Charlotte is a surveyor mapping a triangular plot of land. She measures two sides of the triangle as 14 meters and 19 meters, and the angle between these two sides is 48°. She needs to determine the length of the third side to complete her map. What is the length of the third side, rounded to the nearest meter?
3. In triangle ABC, side a = 16, side b = 11, and angle C = 60°. Find side c.

…and 5 more problems