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, FSc Part1, Important Questions FSc 1