JEE Mains · Maths · STD 11 - Trigonometrical equations
The angle of elevation of the top of vertical tower standing on a horizontal plane is observed to be \(45^o\) from a point \(A\) on the plane. Let \(B\) be the point \(30\, m\) vertically above the point \(A\). If the angle of elevation of the top of the tower from \(B\) be \(30^o\), then the distance (in \(m\)) of the foot of the tower from the point \(A\) is:
- A \(15\left( {1 + \sqrt 3 } \right)\)
- B \(15\left( {3 - \sqrt 3 } \right)\)
- C \(15\left( {3 + \sqrt 3 } \right)\)
- D \(15\left( {5 - \sqrt 3 } \right)\)
Answer & Solution
Correct Answer
(C) \(15\left( {3 + \sqrt 3 } \right)\)
Step-by-step Solution
Detailed explanation
\(AB = 30\,m\, = NP\) In \(\Delta ANM\,\,\tan {45^o}\, = \frac{{MN}}{{AN}}\, = 1\) \( \Rightarrow \,MN = AN\) \(PM = MN - 30\) \( = AN - 30\) In \(\Delta BPM\,\,\tan \,{30^o}\, = \,\frac{{PM}}{{PB}}\, = \,\frac{{AN - 30}}{{AN}}\)…
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
- If the area of the triangle formed by the positive \(x-\)axis, the normal and the tangent to the circle \((x-2)^{2}+(y-3)^{2}=25\) at the point \((5,7)\) is \(A\) then \(24 A\) is equal to ...... .JEE Mains 2021 Hard
- Let \(S\) be the set of all functions \(f:[0,1] \rightarrow \mathrm{R}\) which are continuous on \([0,1]\) and differentiable on \((0,1) .\) Then for every \(f\) in \(\mathrm{S},\) there exists a \(\mathrm{c} \in(0,1),\) depending on \(f,\) such thatJEE Mains 2020 Hard
- Let \(A\) be the set of first 101 terms of an A.P., whose first term is 1 and the common difference is 5 and let \(B\) be the set of first 71 terms of an A.P., whose first term is 9 and the common difference is 7. Then the number of elements in \(A \cap B\), which are divisible by 3, is :JEE Mains 2026 Hard
- \(25^{190}-19^{190}-8^{190}+2^{190}\) is divisible byJEE Mains 2023 Hard
- If the locus of \(z \in \mathrm{C}\), such that
\(\operatorname{Re}\left(\frac{z-1}{2 z+\mathrm{i}}\right)+\operatorname{Re}\left(\frac{\bar{z}-1}{2 \bar{z}-\mathrm{i}}\right)=2\)
is a circle of radius \(r\) and center \((a, b)\) then \(\frac{15 a b}{r^2}\) is equal to :JEE Mains 2025 Hard - Two circles with equal radii intersecting at the points \((0, 1)\) and \((0, -1).\) The tangent at the point \((0, 1)\) to one of the circles passes through the centre of the other circle. Then the distance between the centres of these circles isJEE Mains 2019 Hard
More PYQs from JEE Mains
- The tangent and normal to the ellipse \(3x^2 + 5y^2 = 32\) at the point \(P(2, 2)\) meet the \(x-\) axis at \(Q\) and \(R,\) respectively. Then the area(in sq. units) of the triangle \(PQR\) isJEE Mains 2019 Hard
- Let the line passing through the points, \(P(2,-1,2)\) and \(Q(5,3,4)\) meet the plane \(x-y+z=4\) at the point \(R\). Then the distance of the point \(R\) from the plane \(x+2 y+3 z+2=0\) measured parallel to the line \(\frac{x-7}{2}=\frac{y+3}{2}=\frac{z-2}{1}\) is equal toJEE Mains 2023 Hard
- Let \(\mathrm{A}=\{1,2,3,4\}\) and \(\mathrm{R}=\{(1,2),(2,3),(1,4)\}\) be a relation on \(\mathrm{A}\). Let \(\mathrm{S}\) be the equivalence relation on \(A\) such that \(\mathrm{R} \subset \mathrm{S}\) and the number of elements in \(\mathrm{S}\) is \(\mathrm{n}\). Then, the minimum value of \(\mathrm{n}\) is ...........JEE Mains 2024 Easy
- Let \(\mathrm{f}:(-1, \infty) \rightarrow \mathrm{R}\) be defined by \(\mathrm{f}(0)=1\) and \(f(x)=\frac{1}{x} \log _{e}(1+x), x \neq 0 .\) Then the function \(f\)JEE Mains 2020 Hard
- Let \(z\) be complex number such that \(\left|\frac{z-i}{z+2 i}\right|=1\) and \(|z|=\frac{5}{2} \cdot\) Then the value of \(|z+3 i|\) isJEE Mains 2020 Hard
- If the chord joining the points \(P_{1}(x_{1},y_{1})\) and \(P_{2}(x_{2},y_{2})\) on the parabola \(y^{2}=12x\) subtends a right angle at the vertex of the parabola, then \(x_{1}x_{2}-y_{1}y_{2}\) is equal toJEE Mains 2026 Hard