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Class 9Class 10First YearSecond Year
$1. Given m \overline{A C}=1 \mathrm{~cm} m \overline{B C}=2 \mathrm{~cm} m \angle C=120^{\circ} .Compute the length A B and the area of \triangle A B C .Hint: (A B)^{2}=(A C)^{2}+(B C)^{2}+2 m A C . m C D where (m \overline{C D})=(m \overline{B C}) \cos \left(180^{\circ}-m \angle C\right) (Use theorem 1).$

$9. Whether the triangle with sides 5 \mathrm{~cm} 7 \mathrm{~cm} 8 \mathrm{~cm} is acute obtuce or right angled.$

$6. In a triangle A B C m \overline{B C}=21 \mathrm{~cm} . m \overline{A C}=17 \mathrm{~cm} m \overline{A B}=10 \mathrm{~cm} . Calculate the projection of \overline{A B} upon \overline{B C} .$

$8. In a \triangle A B C a=17 \mathrm{~cm} b=15 \mathrm{~cm} and c=8 \mathrm{~cm} find m \angle B .$

$3. In a \triangle A B C calculate m \overline{B C} when m \overline{A B}=5 \mathrm{~cm} m \overline{A C}=4 \mathrm{~cm} m \angle A=60^{\circ} .$

$4. In a \triangle A B C calculate m \overline{A C} when m \overline{A B}=5 \mathrm{~cm} m \overline{B C}=4 \sqrt{2} \mathrm{~cm} m \angle B=45^{\circ} .$

$1. In a \triangle A B C m \angle A=60^{\circ} prove that (B C)^{2}=(A B)^{2}+(A C)^{2}-m \overline{A B} \cdot m \overline{A C} .$