JEE Mains · Maths · STD 11 - Trigonometrical equations
Let \(10\) vertical poles standing at equal distances on a straight line, subtend the same angle of elevation at a point \(O\) on this line and all the poles are on the same side of \(O\). If the height of the longest pole is \('h'\) and the distance of the foot of the smallest pole from \(O\) is \('a'\); then the distance between two consecutive poles, is
- A \(\frac{{h\,\cos \,\alpha - a\,\sin \,\alpha }}{{9\,\sin \,\alpha }}\)
- B \(\frac{{h\,\sin \,\alpha + a\,\cos \,\alpha }}{{9\,\sin \,\alpha }}\)
- C \(\frac{{h\,\cos \,\alpha - a\,\sin \,\alpha }}{{9\,\cos \,\alpha }}\)
- D \(\frac{{h\,\sin \,\alpha - a\,\cos \,\alpha }}{{9\,\cos \,\alpha }}\)
Answer & Solution
Correct Answer
(A) \(\frac{{h\,\cos \,\alpha - a\,\sin \,\alpha }}{{9\,\sin \,\alpha }}\)
Step-by-step Solution
Detailed explanation
\(\Delta O{A_1}{B_1},\,\,\Delta O{A_2}{B_2},\,\,\Delta O{A_3}{B_3},........,\) \(\Delta O{A_{10}}{B_{10}}\) all are similar triangles.…
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 sum of all \(3 -\)digit numbers less than or equal to \(500,\) that are formed without using the digit \("1"\) and they all are multiple of \(11 ,\) is ..... .JEE Mains 2021 Hard
- Two tangents are drawn from the point \(\mathrm{P}(-1,1)\) to the circle \(\mathrm{x}^{2}+\mathrm{y}^{2}-2 \mathrm{x}-6 \mathrm{y}+6=0\). If these tangents touch the circle at points \(A\) and \(B\), and if \(D\) is a point on the circle such that length of the segments \(A B\) and \(A D\) are equal, then the area of the triangle \(A B D\) is eqaul to:JEE Mains 2021 Medium
- The value of the integral \(\int\limits_{ - 2}^2 {\frac{{{{\sin }^2}\,x}}{{\left[ {\frac{x}{\pi }} \right] + \frac{1}{2}}}\,\,dx} \) (where \([x]\) denotes the greatest integer less than or equal to \(x\) ) isJEE Mains 2019 Hard
- The sum of the series \(\frac{1}{1-3 \cdot 1^2+1^4}+\) \(\frac{2}{1-3 \cdot 2^2+2^4}+\frac{3}{1-3 \cdot 3^2+3^4}+\ldots\). up to \(10\) terms isJEE Mains 2024 Hard
- In a triangle \(\mathrm{ABC}\), if \(|\overrightarrow{\mathrm{BC}}|=3,|\overrightarrow{\mathrm{C}}|=5\) and \(|\overrightarrow{\mathrm{BA}}|=7\), then the projection of the vector \(\overline{\mathrm{BA}}\) on \(\overline{\mathrm{BC}}\) is equal to:JEE Mains 2021 Easy
- There are \(3\) sections in a question paper and each section contains \(5\) questions. A candidate has to answer a total of \(5\) questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, isJEE Mains 2020 Medium
More PYQs from JEE Mains
- If the image of the point \((-4,5)\) in the line \(x+2 y=2\) lies on the circle \((x+4)^2+(y-3)^2=r^2\), then \(r\) is equal lo:JEE Mains 2024 Medium
- \(\mathop {\lim }\limits_{y \to 0} \frac{{\sqrt {1 + \sqrt {1 + {y^4}} } - \sqrt 2 }}{{{y^4}}} = \)JEE Mains 2019 Hard
- The number of real roots of the equation \(\mathrm{e}^{4 \mathrm{x}}-\mathrm{e}^{3 \mathrm{x}}-4 \mathrm{e}^{2 \mathrm{x}}-\mathrm{e}^{\mathrm{x}}+1=0\) is equal to \(.....\)JEE Mains 2021 Medium
- Let \(A = \begin{bmatrix} 1 & 2 \\ 1 & \alpha \end{bmatrix}\) and \(B = \begin{bmatrix} 3 & 3 \\ \beta & 2 \end{bmatrix}\). If \(A^2 - 4A + I = O\) and \(B^2 - 5B - 6I = O\), then among the two statements :
(S1): \([(B-A)(B+A)]^T = \begin{bmatrix} 13 & 15 \\ 7 & 10 \end{bmatrix}\)
and
(S2): \(\det(\text{adj}(A+B)) = -5\),JEE Mains 2026 Hard - Let \(\alpha\) be the area of the larger region bounded by the curve \(y ^2=8 x\) and the lines \(y = x\) and \(x =2\), which lies in the first quadrant. Then the value of \(3 \alpha\) is equal to \(..............\).JEE Mains 2023 Hard
- A chord is drawn through the focus of the parabola \(y^2\, = 6x\) such that its distance from the vertex of this parabola is \(\frac{{\sqrt 5 }}{2}\) , then its slope can be:JEE Mains 2014 Hard