JEE Mains · Maths · STD 11 - Trigonometrical equations
Two vertical poles \(AB =15 m\) and \(CD =10 m\) are standing apart on a horizontal ground with points \(A\) and \(C\) on the ground. If \(P\) is the point of intersection of \(BC\) and \(AD ,\) then the height of \(P\) (in \(m\) ) above the line \(AC\) is
- A \(\frac{20}{3}\)
- B \(5\)
- C \(\frac{10}{3}\)
- D \(6\)
Answer & Solution
Correct Answer
(D) \(6\)
Step-by-step Solution
Detailed explanation
\(\tan \theta=\frac{10}{x}=\frac{h}{x_{2}} \Rightarrow x_{2}=\frac{h x}{10}\) \(\tan \phi=\frac{15}{x}=\frac{h}{x_{1}} \Rightarrow x_{1}=\frac{h x}{15}\) Now, \(x_{1}+x_{2}=x=\frac{h x}{15}+\frac{h x}{10}\) \(\Rightarrow 1=\frac{h}{10}+\frac{h}{15} \Rightarrow h=6\)
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 sum of the coefficients in the expansion of \((x+y)^{n}\) is \(4096,\) then the greatest coefficient in the expansion is .... .JEE Mains 2021 Medium
- Let the tangent to the circle \(x^{2}+y^{2}=25\) at the point \(R (3,4)\) meet \(x\) -axis and \(y\) -axis at point \(P\) and \(Q\), respectively. If \(r\) is the radius of the circle passing through the origin \(O\) and having centre at the incentre of the triangle \(OPQ ,\) then \(r ^{2}\) is equal toJEE Mains 2021 Hard
- The number of elements in the set \(S =\left\{\theta \in[0,2 \pi]: 3 \cos ^4 \theta-5 \cos ^2 \theta-2 \sin ^6 \theta+2=0\right\}\) is \(...........\).JEE Mains 2023 Hard
- If \(\theta \in[-2 \pi, 2 \pi]\), then the number of solutions of \(2 \sqrt{2} \cos ^2 \theta+(2-\sqrt{6}) \cos \theta-\sqrt{3}=0\), is equal to:JEE Mains 2025 Easy
- Let \(\vec{a}=\hat{i}+2 \hat{j}+3 \hat{k}, \quad \vec{b}=2 \hat{i}+3 \hat{j}-5 \hat{k} \quad\) and \(\overrightarrow{\mathrm{c}}=3 \hat{\mathrm{i}}-\hat{\mathrm{j}}+\lambda \hat{\mathrm{k}}\) be three vectors. Let \(\overrightarrow{\mathrm{r}}\) be a unit vector along \(\vec{b}+\vec{c}\). If \(\vec{r} . \vec{a}=3\), then \(3 \lambda\) is equal to :JEE Mains 2024 Medium
- If for \(x \in \left( {0,\frac{1}{4}} \right)\) , the derivative of \({\tan ^{ - 1}}\left( {\frac{{6x\sqrt x }}{{1 - 9{x^3}}}} \right)\) is \(\sqrt x \cdot g\left( x \right)\) then \(g\left( x \right)\) equals:JEE Mains 2017 Hard
More PYQs from JEE Mains
- Let \(y=y(x)\) be the solution curve of the differential equation \(\frac{ dy }{ dx }+\left(\frac{2 x ^{2}+11 x +13}{ x ^{3}+6 x ^{2}+11 x +6}\right)\) \(y=\frac{(x+3)}{x+1}, x>-1\), which passes through the point \((0,1)\). Then \(y (1)\) is equal to.JEE Mains 2022 Hard
- The sum, \(\sum\limits_{n=1}^{7} \frac{n(n+1)(2 n+1)}{4}\) is equal toJEE Mains 2020 Medium
- Let \( \vec{a}=2\hat{i}-5\hat{j}+5\hat{k} \) and \( \vec{b}=\hat{i}-\hat{j}+3\hat{k}. \) If \( \vec{c} \) is a vector such that
\( 2(\vec{a}\times\vec{c})+3(\vec{b}\times\vec{c})=\vec{0} \) and \( (\vec{a}-\vec{b})\cdot\vec{c}=-97, \) then \( |\vec{c}\times \hat{k}|^{2} \) is equal toJEE Mains 2026 Easy - The value of \(\int\limits_{0}^{2\pi } {\left[ {\sin \,2x\left( {1 + \cos \,3x} \right)} \right]} \,dx\) where \([t]\) denotes the greatest integer function, isJEE Mains 2019 Hard
- If in a triangle \(\mathrm{ABC}, \mathrm{AB}=5\) units, \(\angle \mathrm{B}=\cos ^{-1}\left(\frac{3}{5}\right)\) and radius of circum circle of \(\triangle \mathrm{ABC}\) is \(5\) units, then the area (in sq. units) of \(\triangle \mathrm{ABC}\) is:JEE Mains 2021 Hard
- Let \(y(x)\) be the solution of the differential equation \(2 x^{2} d y+\left(e^{y}-2 x\right) d x=0, x>0\). If \(y(e)=1\), then \(\mathrm{y}(1)\) is equal to :JEE Mains 2021 Hard