Question
In $\triangle\text{PQR},$ right-angled at $Q, PQ = 3\ cm$ and $PR = 6\ cm.$ Determine $\angle\text{P}$ and $\angle\text{R}.$

Answer


From above figure
$\sin\text{R}=\frac{\text{PQ}}{\text{PR}}$
$\sin\text{R}=\frac{3}{6}=\frac{1}{2}$
$\therefore\ \sin\text{R}=\sin30^\circ$
$\text{R}=\sin30^\circ$
We Know in $\triangle\text{le }\angle\text{P}+\angle\text{Q}+\angle\text{R}=180^\circ$
$\angle\text{P}+90^\circ+30^\circ=180^\circ$
$\angle\text{P}=60^\circ$

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

Fill in the blanks in the following table, given that $a$ is the first term, $d$ is the common difference and $a_n$ is the $n^{th}$  term of the $AP:$
  $a$ $d$ $n$ $a_n$
$i$ $7$ $3$ $8$ $...$
$ii$ $-18$ $...$ $10$ $0$
$iii$ $...$ $-3$ $18$ $-5$
$iv$ $-18.9$ $2.5$ $...$ $3.6$
$v$ $3.5$ $0$ $105$ $...$
Is the given series $2, 4, 8, 16, ......$ form an AP? If It forms an AP, then find the common difference d and write the next three terms.
In the following figure, shows a sector of a circle, centre $O,$ containing an angle $\theta^\circ.$ Prove that:
Area of the shaded region is $\frac{\text{r}^2}{2}\Big(\tan\theta-\frac{\pi\theta}{180}\Big)$
A piggy bank contains hundred $50$ p coins, fifty ₹ $1 $coins, twenty ₹ $2$ coins and ten ₹ 5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin
  1. will be a $50$ p coin?
  2. will not be a ₹ $5$ coin?
A right cylindrical vessel is full of water. How many right cones having the same radius and height as those of the right cylinder will be needed to store that water$?$
$PQ$ is a chord of length $4.8\ cm$ of a circle of radius $3\ cm$. The tangent at $P$ and $Q$ intersect at a point $T$ as shown in the figure. Find the length of $TP.$
The angle of depression from the top of a tower of a point $A$ on the ground is $30^\circ .$ On moving a distance of $20$ metres from the point $A$ towards the foot of the tower to a point $B,$ the angle of elevation of the top of the tower from the point $B$ is $60^\circ $. Find the height of the tower and its distance from the point $A.$
Very-Short and Short-Answer Questions:
Write the number of solutions of the following pair of linear equations:
$x + 2y - 8 = 0,$
$2x + 4y = 16$
Prove that following numbers are irrationals:
$\frac{3}{2\sqrt{5}}$
During the medical check-up of 35 students of a class, their weights were recorded as follows:
Weight (in kg)
No. of students
Less than 38
0
Less than 40
3
Less than 42
5
Less than 44
9
Less than 46
14
Less than 48
28
Less than 50
32
Less than 52
35
Draw a less than type ogive for the given data. Hence, obtain the median weight from the graph and verify the result by using the formula