JEE Mains · Maths · STD 11 - Trigonometrical equations
Consider a triangular plot \(ABC\) with sides \(AB = 7\, m\), \(BC = 5\, m\) and \(CA = 6\, m\). A vertical lamp-post at the mid point \(D\) of \(AC\) subtends an angle \(30^o\) at \(B\). The height (in \(m\)) of the lamp-post is
- A \(\frac{3}{2}\,\sqrt {21} \)
- B \(\frac{2}{3}\,\sqrt {21} \)
- C \(2\sqrt {21} \)
- D \(7\sqrt {21} \)
Answer & Solution
Correct Answer
(B) \(\frac{2}{3}\,\sqrt {21} \)
Step-by-step Solution
Detailed explanation
Length of median \(BM\,=\,\frac {1}{2}\,\sqrt {2(BC^2+BA^2)-(AC)^2}\) \(=\,\frac {1}{2}\sqrt {2(25+49)-36}\) \(=\frac {1}{2}\sqrt {112}\) \(=\,\sqrt {\frac {112}{4}}\) \(\sqrt {28}\) \(=\,2\sqrt 7\) Let \(h\) be height of tower, given \(\tan 30^o\,=\,\frac {h}{2\sqrt h}\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The mirror image of the point \((1,2,3)\) in a plane is \(\left(-\frac{7}{3},-\frac{4}{3},-\frac{1}{3}\right) .\) Which of the following points lies on this plane ?JEE Mains 2020 Hard
- Let \(\displaystyle\int_{-2}^{2} (|\sin x| + [x \sin x])\,dx = 2(3 - \cos 2) + \beta\), where \([\cdot]\) is the greatest integer function. Then \(\beta \sin\left(\dfrac{\beta}{2}\right)\) equals:JEE Mains 2026 Medium
- Let \(S=\left\{p_1, p_2 \ldots ., p_{10}\right\}\) be the set of first ten prime numbers. Let \(A=S \cup P\), where \(P\) is the set of all possible products of distinct elements of \(S\). Then the number of all ordered pairs ( \(x, y\) ), \(x \in S\), \(y \in A\), such that \(x\) divides \(y\), is ______.JEE Mains 2025 Medium
- Let the equation of the circle, which touches \(x\)-axis at the point \((a, 0), a\gt0\) and cuts off an intercept of length \(b\) on \(y\)-axis be \(x^2+y^2-\alpha x+\beta y+\gamma=0\). If the circle lies below \(x\)-axis, then the ordered pair \(\left(2 a, b^2\right)\) is equal toJEE Mains 2025 Medium
- Consider the following system of equations : \(x+2 y-3 z=a\) ; \(2 x+6 y-11 z=b\) ; \(x-2 y+7 z=c\) where \(a , b\) and \(c\) are real constants. Then the system of equations :JEE Mains 2021 Medium
- If \(x\, = \,{\sin ^{ - 1}}(\sin \,10)\) and \(y = \,{\cos ^{ - 1}}\,(\cos \,10)\) , then \(y -x\) is equal toJEE Mains 2019 Hard
More PYQs from JEE Mains
- Consider a circle \(C_1: x^2+y^2-4 x-2 y=\alpha-5\).Let its mirror image in the line \(y=2 x+1\) be another circle \(C _2: 5 x ^2+5 y ^2-10 fx -10 gy +36=0\).Let \(r\) be the radius of \(C _2\). Then \(\alpha+ r\) is equal to \(......\).JEE Mains 2023 Hard
- If \(y = f(x)\) is the solution of the differential equation \(\frac{{dy}}{{dx}} = \left( {\tan \,x - y} \right){\sec ^2}\,x,\,x \in \left( { - \frac{\pi }{2},\frac{\pi }{2}} \right)\), such that \(y(0) = 0\), then \(y\left( { - \frac{\pi }{4}} \right)\) is equal toJEE Mains 2019 Hard
- Let \(\mathrm{I}(x)=\int \frac{d x}{(x-11)^{\frac{11}{13}}(x+15)^{\frac{15}{13}}}\). If \(\mathrm{I}(37)-\mathrm{I}(24)=\frac{1}{4}\left(\frac{1}{\mathrm{~b}^{\frac{1}{13}}}-\frac{1}{\mathrm{c}^{\frac{1}{13}}}\right), \mathrm{b}, \mathrm{c} \in \mathrm{N}\), then \(3(\mathrm{~b}+\mathrm{c})\) is equal toJEE Mains 2025 Hard
- Let \(f (x) = a^x (a > 0)\) be written as \(f( x) = f_1( x) + f_2( x)\) , where \(f_1( x)\) is an even function and \(f_2( x)\) is an odd function. Then \(f_1( x + y) + f_1( x - y )\) equalsJEE Mains 2019 Hard
- Let \(A=\left(\begin{array}{ccc}1 & 0 & 0 \\ 0 & 4 & -1 \\ 0 & 12 & -3\end{array}\right)\). Then the sum of the diagonal elements of the matrix \(( A + I )^{11}\) is equal to:JEE Mains 2023 Hard
- Let \(S\) be the set of all real roots of the equation, \(3^{x}\left(3^{x}-1\right)+2=\left|3^{x}-1\right|+\left|3^{x}-2\right| .\) Then \(\mathrm{S}\)JEE Mains 2020 Hard