# Law of Sines and Cosines Worksheet

Law of Sines and Cosines Worksheet
• Page 1
1.
For any parallelogram, find the ratio of sum of the squares of the lengths of the diagonals to the sum of the squares of the lengths of two adjacent sides.

 a. 3 b. 2 c. 1 d. $\frac{1}{2}$

2.
In ΔDEF, if $\angle$$E$ = 30°, $d$ = 21.4, and $f$ = 10.6, then Find $\angle$D to the nearest ten minutes.

 a. 54°30′ b. 35°30′ c. 5°25′ d. 53°44′

3.
In ΔDEF, if $\angle$E = 35°, $\angle$D = 65°, and $f$ = 15 units, then find the length of $d$ to three significant digits.
 a. 15.287 units b. 13.799 units c. 17.345 units d. 16.523 units

4.
In triangle DEF, if $\angle$E = 54o30', $d$ = 21.4, and $f$ = 10.6, then Find $\angle$D to the nearest ten minutes.

 a. 5°25′ b. 54°30′ c. 35°30′ d. 84°35′

5.
In ΔPQR, if $\angle$Q = 62o, $p$ = 15, and $r$ = 12, then find $\angle$P to the nearest degree.

 a. 55° b. 71° c. 19° d. 109°

6.
In ΔPQR, if $\angle$Q = 70o, $p$ = 15, $q$ = 20, then find $\angle$R to the nearest degree.
 a. 65o b. 15o c. 70o d. can′t be determined

7.
In ΔABC, if $\angle$A = 52o, $a$ = 14 in., $b$ = 8 in., then find the length of $c$ to the nearest two significant digits.
 a. 19 in. b. 17 in. c. 10 in. d. 14 in.

8.
In ΔDEF, if $\angle$E = 34o20', $\angle$D = 68o30' and $f$ = 16.5 units, then find the length of $d$ to three significant digits.
 a. 16.5 units b. 17.3 units c. 15.7 units d. 15.2 units

9.
In ΔABC, if $\angle$C = 63.2o, $b$ = 8.7cm and $a$ = 18.2cm, then find the area of triangle to three significant digits.
 a. 79.2sq.cm b. 35.7sq.cm c. 19.8sq.cm d. 70.7sq.cm

In ΔDEF, if $\angle$E = 42o, $\angle$F = 78o and $f$ = 14, then find the area of triangle DEF to two significant digits.