# Ch 12: Applications of Trigonometry

• Find the value of $tan\frac{\alpha}{2}$ in term of $s$ — BISE Gujrawala(2015)
• Solve $\triangle ABC$ if $b=125$, $r=53^{\circ}$, $\alpha=47^{\circ}$ — BISE Gujrawala(2015)
• Show that $r_1=stan\frac{\alpha}{2}$ — BISE Gujrawala(2015)
• Define an escribed circle.— BISE Gujrawala(2015)
• With usual notation prove that $r_1+r_2+r_3-r=4R$ — BISE Gujrawala(2015)
• In $\triangle ABC$ $r=90^{\circ}$, $\alpha=62^{\circ}40'$, $b=796$, find $\beta$ anf $a$— BISE Gujrawala(2017)
• Find the area of $\triangle ABC$, if $a=18$, $b=24$,$c=30$ — BISE Gujrawala(2017)
• Prove that $\frac{1}{r^2}+\frac{1}{{r_1}^2}+\frac{1}{{r_2}^2}+\frac{1}{{r_3}^2}=\frac{a^2+b^2+c^2}{\triangle^2}$ — BISE Gujrawala(2017)
• Show that $r_2=s tan\frac{\beta}{2}$— BISE Sargodha(2015)
• Show that $r=(s-a)tan\frac{\alpha}{2}$— BISE Sargodha(2015)
• The sides of a triangle are $x^2+x+1$,$2x+1$ and $x^2-1$. Prove that the greatest angle of the triangle is $120^{\circ}$ — BISE Sargodha(2015), FBISE(2017)
• Solve the triangle $ABC$, if $\beta=60^{\circ}$, $\gamma=15^{\circ}$, $b=\sqrt{6}$— BISE Sargodha(2015)
• Find the area of the triangle $ABC$, when $a=18$, $b=24$, $c=30$ — BISE Sargodha(2015)
• Prove that $r_1r_2r_3=rs^2$— BISE Sargodha(2015)
• Prove that $abc(sin\alpha+sin\beta+sin\gamma)=4\triangle s$— BISE Sargodha(2015)
• With usual notation prove that $cos\frac{\alpha}{2}=\sqrt{\frac{s(s-a)}{bc}}$— BISE Sargodha(2016)
• With usual notation prove that $r=\frac{\triangle}{s}$— BISE Sargodha(2016)
• Prove that in an equilateral triangle $r:R:r_1:r_2:r_3=1:2:3:3:3$— BISE Sargodha(2016)
• At the top of a cliff $80$m high the angle of depression of a boat is $12^{\circ}$. How far is the boat from the cliff? — BISE Lahore(2017)
• Solve the $\triangle ABC$ in which $\alpha=3$, $c=6$ and $\beta=36^{\circ}20'$— BISE Lahore(2017)
• Find the smallest angle of the $\triangle ABC$ in which $\alpha=37.34$, $b=3.24$ and $c=35.06$— BISE Lahore(2017)
• Prove that with usual notation, $R=\frac{abc}{4\triangle}$ — FBISE(2016)
• Show that $r_1=4rsin\frac{\alpha}{2}cos\frac{\beta}{2}cos\frac{\gamma}{2}$ — FBISE(2017)
• Prove that $\frac{1}{r}=\frac{1}{r_1}+\frac{1}{r_2}+\frac{1}{r_3}$— FBISE(2016)
• Prove that in an equilateral triangle $r:R:r_1=1:2:3$ — FBISE(2017)
• fsc-part1-ptb/important-questions/ch12-application-of-trigonometry