Question

Two sides of a parallelogram are 120 degrees with each other. The lengths of the sides

are 10.0 m and 6.5 m. Find the length of the diagonal opposite the included angle.

3. The base of the triangle is 5 m and the base angles are 65 and 40. Find the other side of

the triangle.

Answer 1

Solution.

$\alpha=120^o;$

$a=10.0m;$

$b=6.5m;$

$c^2=a^2+b^2-2abcos\alpha$ ;

$c=\sqrt{100+42.25+2\sdot10\sdot6.5\sdot0.5}=14.4m;$

$3. a=5m;$

$\beta=65^o;$

$\gamma=40^o;$

$\dfrac{a}{sin\alpha}=\dfrac{b}{sin\beta}\implies b=\dfrac{asin\beta}{sin\alpha};$

$b=\dfrac{5\sdot0.9}{0.97}=4.6m;$

$\dfrac{a}{sin\alpha}=\dfrac{c}{sin\gamma}\implies c=\dfrac{asin\gamma}{sin\alpha};$

$c=\dfrac{5\sdot0.64}{0.97}=3.3m;$

Answer:$c=14.4m;$

$3. b=4.6m; c=3.3m.$