Question
Construct a rectangle $\text{ABCCD}, AB = 6\ cm. \angle CAB = 30^\circ .$

Answer

Image
Steps of construction:
$1)$ Draw a line segment $AB = 6\ cm.$
$2)$ On $A$ and $B$ draw perpendiculars $AX$ and $BY$ to $AB.$
$3)$ With $A$ as centre and radius $= BC$ cut an arc on $AX$. Mark it as $D$.
$5)$ Join $CD.$
$6)\text{ABCD}$ is the required rectangle.

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

Similar questions

Draw the graph of a line $2x + 3y = 6$. From the graph, find the slope and $y-$intercept of the line.
Find the amount and the compound interest payable annually on the following :$Rs.32000$ for $2$ years at $7 \frac{1}{2} \%$ per annum.
If $x = (4-\sqrt{15})$, find the values of $x^2+\frac{1}{x^2}$
How much will $Rs. 50,000$ amount to in $3$ years, compounded yearly, if the rates for the successive years are $6\ \%\ , 8\ \%\ $ and $10\ \%\ $ respectively?
If $s=\frac{n}{2}[2 a+(n-1) d]$, the $n$ express $d$ in terms of $s, a$ and $n$, find $d$ if $n=3, a=n+1$ and $s=18$.
Solve the following pair of linear $($simultaneous$)$ equation by the method of elimination by substitution:$1.5x + 0.1y = 6.2;3x - 0.4y = 11.2$
If $2 \sin x = \sqrt{3}$ , evaluate.$( i)4 \sin^3 x - 3 \sin x.(ii)3 \cos x - 4 \cos^3 x.$
One day three friends Amit (A), Binay (B) and Chanchal (C) were playing hide and seek game in the park of their society. Amit and Binay hide in the shrubs and Chanchal has to find both of them. If the position of three friends are at A, B and C respectively, as shown in the figure and forms a right angled triangle ABC such that AB = 6m, $B C=2 \sqrt{3} m$ and $\angle B =90$.
Image
Based on the above information, answer the following questions :
Q.1. The length of AC is :
(a) 4 m (b) $8 \sqrt{3} m$ (c) $5 \sqrt{3} m$ (d) $4 \sqrt{3} m$
Q.2. The measure of $\angle A$ is :
(a) 30 (b) 45 (c) 60 (d) 90
Q.3. The measure of $\angle C$ is :
(a) 30 (b) 45 (c) 60 (d) 90
Q.4. $\cos 2 A$ is equal to :
(a) 1 (b) $\frac{1}{2}$ (c) $\frac{\sqrt{3}}{2}$ (d) $\sqrt{3}$
Q.5. $2 \sin \left(\frac{ C }{2}\right)$ is equal to :
(a) 1 (b) $\frac{1}{2}$ (c) $\sqrt{3}$ (d) $\frac{\sqrt{3}}{2}$
Of the two numbers, 4 times the smaller one is less than 3 times the larger one by 6. Also, the sum of the numbers is larger than 6 times their difference by 5. Find the numbers.
A briefcase was sold at a profit of $15\%$. If its cost price was $5\%$ less and it was sold for $Rs.35$ less, the gain would have been $20\%$. Find the cost price of the briefcase.