JEE Mains · Maths · STD 11 - Trigonometrical equations
The angle of elevation of the top of a hill from a point on the horizontal plane passing through the foot of the hill is found to be \(45^{\circ} .\) After walking a distance of \(80\) meters towards the top, up a slope inclined at an angle of \(30^{\circ}\) to the horizontal plane, the angle of elevation of the top of the hill becomes \(75^{\circ} .\) Then the height of the hill (in meters) is
- A \(40\)
- B \(80\)
- C \(120\)
- D \(160\)
Answer & Solution
Correct Answer
(B) \(80\)
Step-by-step Solution
Detailed explanation
\(\tan 75^{\circ}=\frac{ h }{ h +40-40 \sqrt{3}}\) \(\frac{2+\sqrt{3}}{1}=\frac{ h }{ h +40-40 \sqrt{3}}\) \(\Rightarrow 2 h +80-80 \sqrt{3}+\sqrt{3} h +40 \sqrt{3}-120= h\) \(\Rightarrow h (\sqrt{3}+1)=40+40 \sqrt{3}\) \(\Rightarrow h =40\) \(\therefore\) Height of hill…
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
- Let \(R\) be the focus of the parabola \(y^2=20 x\) and the line \(y=m x+c\) intersect the parabola at two points \(P\) and \(Q\). Let the point \(G(10,10)\) be the centroid of the triangle \(P Q R\). If \(c-m=6\), then \(( PQ )^2\) isJEE Mains 2023 Hard
- A spherical iron ball of \(10 \;\mathrm{cm}\) radius is coated with a layer of ice of uniform thickness the melts at a rate of \(50\; \mathrm{cm}^{3} / \mathrm{min}\). When the thickness of ice is \(5 \;\mathrm{cm},\) then the rate (in \(\mathrm{cm} / \mathrm{min.}\) ) at which of the thickness of ice decreases, isJEE Mains 2020 Medium
- If the image of point \(P( 2, 3)\) in a line \(L\) is \(Q( 4, 5)\), then the image of point \(R(0, 0)\) in the same line isJEE Mains 2013 Hard
- Let \(y=y(x)\) be the solution of the differential equation \(2 \cos x \frac{\mathrm{~d} y}{\mathrm{~d} x}=\sin 2 x-4 y \sin x, x \in\left(0, \frac{\pi}{2}\right)\). If \(y\left(\frac{\pi}{3}\right)=0\), then \(y^{\prime}\left(\frac{\pi}{4}\right)+y\left(\frac{\pi}{4}\right)\) is equal to ________.JEE Mains 2025 Easy
- The area of the region enclosed by the parabola \(y=4 x-x^2\) and \(3 y=(x-4)^2\) is equal toJEE Mains 2024 Medium
- The distance of the point \(P (4,6,-2)\) from the line passing through the point \((-3,2,3)\) and parallel to a line with direction ratios \(3,3,-1\) is equal to :JEE Mains 2023 Medium
More PYQs from JEE Mains
- If the domain of the function
\(f(x)=\log _e\left(\frac{2 x-3}{5+4 x}\right)+\sin ^{-1}\left(\frac{4+3 x}{2-x}\right) \quad \text { is } \quad[\alpha, \beta)\)
then \(\alpha^2+4 \beta\) is equal toJEE Mains 2025 Medium - Let \( \vec a ,\vec b\) and \(\vec c \) be three non-zero vectors such that no two of them are collinear and \(\left( {\vec a \times \vec b} \right) \times \vec c = \frac{1}{3}\left| \vec b \right|\left| \vec c \right|\vec a\). If \(\theta \) is the angle between vectors \(\vec b\) and \(\vec c\) , then a value of \(\sin \theta \) is :JEE Mains 2015 Hard
- Let a vector \(\vec{a}\) be coplanar with vectors \(\vec{b}=2 \hat{i}+\hat{j}+\hat{k}\) and \(\vec{c}=\hat{i}-\hat{j}+\hat{k} .\) If \(\vec{a}\) is perpendicular to \(\vec{d}=3 \vec{i}+2 \hat{j}+6 \hat{k}\), and \(|\vec{a}|=\sqrt{10} .\) Then a possible value of \([\overrightarrow{\mathrm{a}} \overrightarrow{\mathrm{b}} \overrightarrow{\mathrm{c}}]+[\overrightarrow{\mathrm{a}} \overrightarrow{\mathrm{b}} \vec{d}]+[\overrightarrow{\mathrm{a}} \vec{c} \vec{d}]\) is equal to:JEE Mains 2021 Hard
- lf Rolle's theorem holds for the function \(f(x) =2x^3 + bx^2 + cx, x \in [-1, 1],\) at the point \(x = \frac {1}{2},\) then \(2b+ c\) equalsJEE Mains 2015 Medium
- Let \(A=\left[\begin{array}{ccc}\cos \theta & 0 & -\sin \theta \\ 0 & 1 & 0 \\ \sin \theta & 0 & \cos \theta\end{array}\right]\). If for some \(\theta \in(0, \pi)\), \(A^2=A^T\), then the sum of the diagonal elements of the matrix \((\mathrm{A}+\mathrm{I})^3+(\mathrm{A}-\mathrm{I})^3-6 \mathrm{~A}\) is equal to _____ .JEE Mains 2025 Easy
- In a group of 3 girls and 4 boys, there are two boys \(B_1\) and \(B_2\). The number of ways, in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but \(B_1\) and \(B_2\) are not adjacent to each other, is :JEE Mains 2025 Medium