Download Solving Triangles Unit Test

Solving Triangles Unit Test
For each of the following triangles give side lengths to two decimal places and angles to
the nearest degree. Each question is worth 5 marks.
1. In KEJ, K  113, E  16 , and k = 9.6 cm. Solve the triangle.
2. In ABC, a = 7.6 cm, b = 7.0 cm and c = 8.2 cm. Solve the triangle.
3. In SAD A  30, D  65 , and a = 16 cm. Solve the triangle.
4. HCS has h = 15 m, c = 21.2 m and S  111 . Solve the triangle.
5. In BET b = 15.0, e = 12.0 and t = 14.0. Solve for the largest angle in the triangle.
(3 marks)
6. For the following triangles (in the ambiguous case) state how many possible solutions
there are and how you know that! If there is no solution state so as your answer. (20
marks)
a) ABC: A  71 , a = 12.2, b = 11.4
b) DEF: D  55 , d = 7.1, e = 9.6
c) GHI: G  118 , g = 13.2, h = 8.3
d) PQR has P  65 , q = 5.5, p = 5.0
7. Calculate the distance, AB as shown in the diagram. (5 marks)
8. Calculate the area of the following triangles to two decimal places. (3 marks each)
a) A triangle has two sides measuring 13 units and 11 units, and the angle included by
these two sides is 44°.
b) A large triangular flag measures 2m x 5m x 4 m. What is its area?
c) A triangle has a side 12.3 m long enclosed by two angles, one measuring 37 degrees
the other 82 degrees. What is the area of this triangle?
9.. For security reasons, a triangular area has been roped off, and three security guards,
Hamish, Narish, and Gwen, each stand at one corner of the roped off area. The angle
formed by the rope at Gwen’s corner is 75°, while the angle formed at Narish’s corner is
64°. If the length of rope between Gwen and Narish is 15 m, then what is the length of
the rope between Gwen and Hamish? (5 marks)
Bonus – for a possible two bonus marks completely prove the Law of Cosines. For a
possible one bonus mark, completely prove the Law of Sines.