Sample QuestionsSine and Cosine Formulae and Their Applications questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
In a triangle ABC, a = 4, b = 3, $\angle\text{A}=60^{\circ}$ then c is a root of the equation:
- ✓
$\text{c}^2-3\text{c}-7=0$
- B
$\text{c}^2+3\text{c}+7=0$
- C
$\text{c}^2-3\text{c}+7=0$
- D
$\text{c}^2+3\text{c}-7=0$
Answer: A.
View full solution →In any $\triangle\text{ABC},2(\text{bc}\cos\text{A + ca}\cos\text{B + ab}\cos\text{C})=$
Answer: C.
View full solution →In any $\triangle\text{ABC},\sum\text{a}^2(\sin\text{B}-\sin\text{C})=$
Answer: D.
View full solution →In a $\triangle\text{ABC},$ if (c + a + b)(a + b − c) = ab, then the measure of angle C is:
- A
$\frac{\pi}{3}$
- B
$\frac{\pi}{6}$
- ✓
$\frac{2\pi}{3}$
- D
$\frac{\pi}{2}$
Answer: C.
View full solution →In the sides of a triangle are in the ratio $1:\sqrt{3}:2,$ then the measure of its greatest angle is:
- A
$\frac{\pi}{6}$
- B
$\frac{\pi}{3}$
- ✓
$\frac{\pi}{2}$
- D
$\frac{2\pi}{3}$
Answer: C.
View full solution →In any triangle ABC, find the value of $\text{a}\sin(\text{B}-\text{C})+\text{b}\sin(\text{C}-\text{A})+\text{c}\sin(\text{A}-\text{B}).$
View full solution →In a $\triangle\text{ABC},$ if $\text{b}=\sqrt{3},$ c = 1 and $\angle\text{A}=30^{\circ},$ find a.
View full solution →If in a $\triangle\text{ABC},\frac{\cos\text{A}}{\text{a}}=\frac{\cos\text{B}}{\text{b}}=\frac{\cos\text{C}}{\text{c}},$ then find the measures of angles A, B, C.
View full solution →In a $\triangle\text{ABC},$ if $\sin\text{A}$ and $\sin\text{B}$ are the roots of the equation $\text{c}^2\text{x}^2-\text{c(a + b) x + ab}=0,$ then find $\angle\text{C}.$
View full solution →Find the area of the triangle $\triangle\text{ABC}$ in which a = 1, b = 2 and $\angle\text{C}=60^{\circ}.$
View full solution →In a $\triangle\text{ABC},$ if a = 5, b = 6 and C = 60°, show that its area is $\frac{15\sqrt{3}}{2}\text{ sq. units.}$
View full solution →If in any $\triangle\text{ABC},\angle\text{C}=105^\circ,\angle\text{B}=45^{\circ},\text{a}=2,$ then find b.
View full solution →$(\text{a}-\text{b})\cos\frac{\text{C}}{2}=\text{c}\sin\Big(\frac{\text{A}-\text{B}}{2}\Big)$
View full solution →$\text{a}(\sin\text{B}-\sin\text{C})+\text{b}(\sin\text{C}-\sin\text{A})+\text{c}(\sin\text{A}-\sin\text{B})=0$
View full solution →$\frac{\cos2\text{A}}{\text{a}^2}-\frac{\cos2\text{B}}{\text{b}^2}=\frac{1}{\text{a}^2}-\frac{1}{\text{b}^2}$
View full solution →$\frac{\text{b}\sec\text{B + c}\sec\text{C}}{\tan\text{B}+\tan\text{C}}=\frac{\text{c}\sec\text{C + a}\sec\text{A}}{\tan\text{C}+\tan\text{A}}=\frac{\text{a}\sec\text{A + b}\sec\text{B}}{\tan\text{A}+\tan\text{B}}.$
View full solution →$\frac{\text{a}^2-\text{c}^2}{\text{b}^2}=\frac{\sin(\text{A}-\text{C})}{\sin(\text{A}+\text{C})}$
View full solution →$\text{b}\sin\text{B}-\text{c}\sin\text{C = a}\sin(\text{B}-\text{C})$
View full solution →$\text{b}\cos\text{B + c}\cos\text{C}=\text{a}\cos(\text{B}-\text{C})$
View full solution →In a $\triangle\text{ABC},$ if a = 18, b = 24, c = 30, find $\cos\text{A},\cos\text{B}$ and $\cos\text{C}.$
View full solution →In $\triangle\text{ABC}$ prove that, it $\theta$ be any angle, then $\text{b}\cos\theta=\text{c}\cos(\text{A}-\theta)+\text{a}\cos(\text{C}+\theta).$
View full solution →If the sides a, b, c of a $\triangle\text{ABC}$ are in H.P., prove that $\sin^2\frac{\text{A}}{2},\sin^2\frac{\text{B}}{2},\sin^2\frac{\text{C}}{2}$ are in H.P.
View full solution →In a $\triangle\text{ABC,}$ if $\sin^2\text{A}+\sin^2\text{B}=\sin^2\text{C},$ show that the triangle is right angled.
View full solution →A person observes the angle of elevation of the peak of a hill from a station to be $\alpha.$ He walks c metres along a slope inclined at an angle $\beta$ and finds the angle of elevation of the peak of the hill to be $\gamma.$ Show that the height of the peak above the ground is $\frac{\text{c}\sin\alpha\sin(\gamma-\beta)}{(\sin\gamma-\alpha)}.$
View full solution →$4\Big(\text{bc}\cos^2\frac{\text{A}}{2}+\text{ca}\cos^2\frac{\text{B}}{2}+\text{ab}\cos^2\frac{\text{C}}{2}\Big)=(\text{a + b + c})^2$
View full solution →