Area of a triangle without a height: sine formula and Heron's formula

Answer Key - Grade 10 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. 1.

   Noah's pizza slice is triangle FGH with FG = 9 in and angle G = 20°. The height FD meets GH at a right angle. To the nearest tenth, how long is FD, in inches?

   3.1
2. 2.

   Pia's tent side is triangle FGH with FG = 13 ft and angle G = 77°. The height FD meets GH at a right angle. To the nearest tenth, how long is FD, in feet?

   12.7
3. 3.

   Ren's garden bed is triangle FGH with FG = 10 m and angle G = 33°. The height FD meets GH at a right angle. To the nearest tenth, how long is FD, in meters?

   5.4
4. 4.

   Tala's paper flag is triangle FGH with FG = 14 cm and angle G = 58°. The height FD meets GH at a right angle. To the nearest tenth, how long is FD, in centimeters?

   11.9
5. 5.

   Zee's sandwich half is triangle FGH with FG = 7 cm, GH = 12 cm, angle G = 80° and angle H = 33°. Which expression gives its area?

   • 7 × 12 × sin 80°
   • ½ × 7 × 12
   • ½ × 7 × 12 × sin 80°
   • ½ × 7 × 12 × sin 33°
6. 6.

   Ari's pennant is triangle FGH with FG = 9 in, GH = 13 in, angle G = 70° and angle H = 40°. Which expression gives its area?

   • ½ × 9 × 13 × sin 70°
   • 9 × 13 × sin 70°
   • ½ × 9 × 13
   • ½ × 9 × 13 × sin 40°
7. 7.

   Jun's sail is triangle FGH with FG = 9 cm and GH = 14 cm. Its height FD is 6.9 cm. To the nearest tenth, what is its area, in square centimeters?

   48.3
8. 8.

   Kira's pizza slice is triangle FGH with FG = 11 in and GH = 16 in. Its height FD is 6.8 in. To the nearest tenth, what is its area, in square inches?

   54.4
9. 9.

   Luz's tent door is triangle FGH with FG = 7 ft and GH = 12 ft. Its height FD is 6.2 ft. To the nearest tenth, what is its area, in square feet?

   37.2
10. 10.

    Milo's picnic lawn is triangle FGH with FG = 13 m and GH = 20 m. Its height FD is 9 m. To the nearest tenth, what is its area, in square meters?

    90