Question Number 188444 by Rupesh123 last updated on 01/Mar/23
Answered by mr W last updated on 01/Mar/23
Commented by mr W last updated on 01/Mar/23
$${a}=\mathrm{2}×\mathrm{1}×\mathrm{sin}\:\frac{\mathrm{48}}{\mathrm{2}}=\mathrm{2}\:\mathrm{sin}\:\mathrm{24} \\ $$$$\frac{{a}}{\mathrm{1}}=\frac{\mathrm{sin}\:\left({x}+\mathrm{66}+\mathrm{42}\right)}{\mathrm{sin}\:\left({x}+\mathrm{66}\right)} \\ $$$$\mathrm{cos}\:\mathrm{42}+\frac{\mathrm{sin}\:\mathrm{42}}{\mathrm{tan}\:\left({x}+\mathrm{66}\right)}=\mathrm{2}\:\mathrm{sin}\:\mathrm{24} \\ $$$$\mathrm{tan}\:\left({x}+\mathrm{66}\right)=\frac{\mathrm{sin}\:\mathrm{42}}{\mathrm{2}\:\mathrm{sin}\:\mathrm{24}−\mathrm{cos}\:\mathrm{42}} \\ $$$$\Rightarrow{x}=\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{sin}\:\mathrm{42}}{\mathrm{2}\:\mathrm{sin}\:\mathrm{24}−\mathrm{cos}\:\mathrm{42}}\right)−\mathrm{66}=\mathrm{18}° \\ $$
Commented by Rupesh123 last updated on 01/Mar/23
Perfect ��