Download App

Trigonometrical Ratios of Standard Angles — MATHEMATICS STD 9 — Question

ICSE BoardEnglish MediumSTD 9MATHEMATICSTrigonometrical Ratios of Standard Angles5 Marks
Question
Find the value of $' y\ '$ if $\sqrt{3}=1.723$.Given your answer correct to $2$ decimal places.
https://pg-data.sgp1.digitaloceanspaces.com/chapter_wise/20822/F50.png" alt="Image" width="250" height="">
✓

Answer

Construction: Draw $BX \perp AE$
Then, $B D=E X=14 \ cm$ and $B X=E D$
$
A X=A E-E X=16-14=2
$
Image
 In right $\triangle AEF$
$ \tan 30^{\circ}=\frac{ FE }{ AE }$
$ \Rightarrow \frac{1}{\sqrt{3}}=\frac{ FE }{16}$
$ \Rightarrow FE =\frac{16}{\sqrt{3}}$
In right $\triangle B D C$,
$\tan 60^{\circ}=\frac{ BD }{ DC }$
$ \Rightarrow \sqrt{3}=\frac{14}{ DC }$
$ \Rightarrow DC =\frac{14}{\sqrt{3}}$
In right $\triangle AXB$,
$\tan 45^{\circ}=\frac{B X}{A X}$
$ \Rightarrow 1=\frac{B X}{2}$
$ \Rightarrow B X=2$
$ \Rightarrow ED = BX =2$
Now,
$y=F C$
$ F E+E D+D C$
$ =\frac{16}{\sqrt{3}}+\frac{14}{\sqrt{3}}+2$
$ =\frac{30+2 \sqrt{3}}{\sqrt{3}}$
$ =\frac{30+3.464}{1.732}$
$ =19.32 .$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "[5 marks sum]" from Trigonometrical Ratios of Standard Angles→Trigonometrical Ratios of Standard Angles — all question types→MATHEMATICS STD 9 question papers→ICSE Board STD 9 question papers→ICSE Board question paper generator→

Similar questions

A publisher gives his distributors a discount of $30\%$ on the printed price of the books. The distributor sells those books to a book seller at $23\%$ discount on the printed price and the book$-$seller sells these books at their printed price. Find the profit percent made by the distributor and the book$-$seller.
→
Construct a quadrilateral $ABCD$ in which $AB = 4.8\ cm, AC = 5.8\ cm, AD = 3.6\ cm, \angle A = 105^\circ $ and $\angle B = 60^\circ $
→
Construct a trapezium $\text{ABCD}$ in which $AB = 4.6\ cm, BC = 6.4\ cm, CD = 5.6\ cm, \angle B = 60^\circ $ and $AD \| BC.$
→
A rectangular field is $80\ m$ long and $50\ m$ wide. A $4\ m$ wide runs through the centre of the field parallel to the length and breadth of the field. Find the total area of the roads.
→
The internal length, breadth, and height of a box are $30 \ cm, 24 \ cm$, and $15 \ cm$. Find the largest number of cubes which can be placed inside this box if the edge of each cube is$;(i) 3 \ cm ;(ii) 4 \ cm ;(iii) 5 \ cm$
→
Find the amount and the compound interest payable annually on the following :$Rs.25000$ for $1 \frac{1}{2}$years at $10\%$ per annum.
→
Arrange the following rational numbers in descending order.$\frac{7}{13}, \frac{8}{15}$, and $\frac{3}{5}$
→
In the following figure $; A C=C D ; \angle B A D=110^{\circ}$ and $\angle A C B=74^{\circ}$.

Prove that: $BC > CD$.
→
Solve :$4 x+\frac{6}{y}=15$ and $3 x-\frac{4}{y}=7$. Hence, find $a$ if $y=a x-2$
→
Rachna borrows $Rs. 12,000$ at $10$ percent per annum interest compounded half$-$yearly. She repays $Rs. 4,000$ at the end of every six months. Calculate the third payment she has to make at end of $18$ months in order to clear the entire loan.
→