Question-43128

Facebook Tweet Pin

Question Number 43128 by Cheyboy last updated on 07/Sep/18

Commented by Cheyboy last updated on 07/Sep/18

$${Find}\:{the}\:{area} \\ $$

Commented by ajfour last updated on 07/Sep/18

$${See}\:{Q}.\mathrm{43131}\:{for}\:{a}\:{possible}\:{solution}. \\ $$

Commented by Cheyboy last updated on 07/Sep/18

$${But}\:{the}\:{working}\:{is}\:{not}\:{shown} \\ $$

Commented by ajfour last updated on 07/Sep/18

$${in}\:{some}\:{time}\:{i}\:{shall}\:{post}. \\ $$

Commented by Cheyboy last updated on 07/Sep/18

$${Ok}\:{sir}\:{thank}\:{you} \\ $$

Answered by behi83417@gmail.com last updated on 07/Sep/18

x^2 =6^2 +7^2 −2×6×7×cosα x^2 =8^2 +11^2 −2×8×11×cosβ 36+49−84cosα=64+121−176cosβ (176+84)cosα=85−185 cosα=((−100)/(260))⇒α=112.62^• S=(1/2)(6×7+8×11).sin112.62= # 60 units.

$${x}^{\mathrm{2}} =\mathrm{6}^{\mathrm{2}} +\mathrm{7}^{\mathrm{2}} −\mathrm{2}×\mathrm{6}×\mathrm{7}×{cos}\alpha \\ $$$${x}^{\mathrm{2}} =\mathrm{8}^{\mathrm{2}} +\mathrm{11}^{\mathrm{2}} −\mathrm{2}×\mathrm{8}×\mathrm{11}×{cos}\beta \\ $$$$\mathrm{36}+\mathrm{49}−\mathrm{84}{cos}\alpha=\mathrm{64}+\mathrm{121}−\mathrm{176}{cos}\beta \\ $$$$\left(\mathrm{176}+\mathrm{84}\right){cos}\alpha=\mathrm{85}−\mathrm{185} \\ $$$${cos}\alpha=\frac{−\mathrm{100}}{\mathrm{260}}\Rightarrow\alpha=\mathrm{112}.\mathrm{62}^{\bullet} \\ $$$${S}=\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{6}×\mathrm{7}+\mathrm{8}×\mathrm{11}\right).{sin}\mathrm{112}.\mathrm{62}= \\ $$$$#\:\:\mathrm{60}\:\:\:{units}. \\ $$

Commented by ajfour last updated on 07/Sep/18