Question 15 Marks
In a rectangle $ABCD , AB =12 cm$ and $\angle BAC =30$. Calculate the lengths of side BC and diagonal AC.
Answer
View full question & answer→$BC =4 \sqrt{3} cm, AC =8 \sqrt{3} cm$.
Questions
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20 questions · timed · auto-graded
Question 25 Marks
In a $\triangle A B C$, right angled at $B$, if $\angle A=30$ and $B C=8 cm$, find the remaining angles and sides.
Answer
View full question & answer→$\angle C =60, AC =16 cm, AB =8 \sqrt{3} cm$
Question 35 Marks
A kite is flying at a height of 120 m from the level ground. It is attached to a string inclined at 60 to the horizontal. Find the length of the string. (Take $\sqrt{3}=1.73$.)
Answer
View full question & answer→138.4 m
Question 45 Marks
A kite is flying with a thread 150 m long. If the thread is assumed stretched straight and makes an angle of 60 with the horizontal, find the height of the kite above the ground. (Take $\sqrt{3}=1.73$.)
Answer
View full question & answer→129.75 m
Question 55 Marks
A ladder leaning against a wall, makes a angle of 60 with the horizontal and the foot of the ladder is 9.5 metres away from the wall. Find the length of the ladder.
Answer
View full question & answer→19 m
Question 65 Marks
A balloon is connected to a meteorological station by a cable of length 200 metres, inclined at 60 to the horizontal. Determine the height of the balloon from the ground, assuming that there is no slack in the string. (Take $\sqrt{3}=1.73$ )
Answer
View full question & answer→173 m
Question 75 Marks
In the figure given below, the rod AB of length 4 inches of a TV disc antena is fixed at right angle to the wall and a rod BC of length 8 inches is supporting the disc.
Based on the above information, answer the following questions :
Q.1. The measure of $\angle ACB$ is :
(a) 30 (b) 45 (c) 60 (d) 90
Q.2. The value of $\tan \angle ABC$ is :
(a) $\frac{1}{\sqrt{3}}$ (b) $\sqrt{3}$ (c) 1 (d) 0
Q.3. The value of $\sin ^2 \angle ACB +\sin ^2 \angle ABC$ is :
(a) $\frac{1}{2}$ (b) 0 (c) 1 (d) not defined
Q.4. The length of AC is :
(a) 6 inches (b) $5 \sqrt{3}$ inches (c) $4 \sqrt{2}$ inches (d) $4 \sqrt{3}$ inches
Q.5. The value of $\sin \angle ACB +\cos \angle ABC +\cot \angle BAC$ is :
(a) 0 (b) 1 (c) 2 (d) not defined
Based on the above information, answer the following questions :
Q.1. The measure of $\angle ACB$ is :
(a) 30 (b) 45 (c) 60 (d) 90
Q.2. The value of $\tan \angle ABC$ is :
(a) $\frac{1}{\sqrt{3}}$ (b) $\sqrt{3}$ (c) 1 (d) 0
Q.3. The value of $\sin ^2 \angle ACB +\sin ^2 \angle ABC$ is :
(a) $\frac{1}{2}$ (b) 0 (c) 1 (d) not defined
Q.4. The length of AC is :
(a) 6 inches (b) $5 \sqrt{3}$ inches (c) $4 \sqrt{2}$ inches (d) $4 \sqrt{3}$ inches
Q.5. The value of $\sin \angle ACB +\cos \angle ABC +\cot \angle BAC$ is :
(a) 0 (b) 1 (c) 2 (d) not defined
Answer
View full question & answer→1. (a) 2. (b) 3. (c) 4. (d) 5. (b)
Question 85 Marks
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 $\angle B =90$.
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) $\frac{\sqrt{3}}{2}$
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) $\frac{\sqrt{3}}{2}$
Answer
View full question & answer→1. (d) 2. (a) 3. (c) 4. (b) 5. (a)
Question 95 Marks
In a rectangle ABCD, AB = 12cm and $\angle$BAC = $30^{\circ}$. Calculate the lengths of side BC and diagonal AC.
Answer
View full question & answer→$BC =4 \sqrt{3} cm, AC =8 \sqrt{3} cm$.
Question 105 Marks
In a $\Delta$ABC, right angled at B, if $\angle$A = $30^{\circ}$ and BC = 8cm, find the remaining angles and sides.
Answer
View full question & answer→$\angle C =60^{\circ}, AC =16 cm, AB =8 \sqrt{3} cm$
Question 115 Marks
A kite is flying at a height of 120 m from the level ground. It is attached to a string inclined at $60^{\circ}$ to the horizontal. Find the length of the string. (Take $\sqrt{3}$ = 1.73)
Answer
View full question & answer→138.4 m
Question 125 Marks
A kite is flying with a thread 150 m long. If the thread is assumed stretched straight and makes an angle of $60^{\circ}$ with the horizontal, find the height of the kite above the ground. (Take $\sqrt{3}$ =1.73.)
Answer
View full question & answer→129.75 m
Question 135 Marks
A ladder leaning against a wall, makes a angle of $60^{\circ}$ with the horizontal and the foot of the ladder is 9.5 metres away from the wall. Find the length of the ladder.
Answer
View full question & answer→19 m
Question 145 Marks
A balloon is connected to a meteorological station by a cable of length 200 metres, inclined at $60^{\circ}$ to the horizontal. Determine the height of the balloon from the ground, assuming that there is no slack in the string. (Take $\sqrt{3}$ = 1.73 )
Answer
View full question & answer→173 m
Question 155 Marks
Answer
View full question & answer→(i) $\frac{12}{13}$ (ii) $\frac{13}{5}$ (iii) $\frac{5}{12}$ (iv) $\frac{4}{5}$ (v) $\frac{5}{3}$ (vi) $\frac{3}{4}$
Question 165 Marks
From the given figure, write down the values of :
(i) sin B (ii) tan B
(iii) cos C (iv) cot C
(v) (sin B cos C + cos B sin C) (vi) $\left(\sec ^2 C -\tan ^2 C \right)$
Answer
View full question & answer→(i) $\frac{8}{17}$ (ii) $\frac{8}{15}$ (iii) $\frac{8}{17}$ (iv) $\frac{8}{15}$ (v) 1 (vi) 1
Question 175 Marks
In the given figure, $\angle$B = $90^{\circ}$, AB = 4 units and BC = 3 units.
Find :
(i) sin A (ii) cos A
(iii) cot A (iv) sin C
(v) sec C (vi) tan C
Answer
View full question & answer→(i) $\frac{3}{5}$ (ii) $\frac{4}{5}$ (iii) $\frac{4}{3}$ (iv) $\frac{4}{5}$ (v) $\frac{5}{3}$ (vi) $\frac{4}{3}$
Question 185 Marks
Look at the figures given below :
From these figures, write down the values of :
(i) sin x (ii) tan x (iii) sec x
(iv) cos y (v) cot y (vi) cosec y
(vii) sin z (viii) cos z (ix) tan z
From these figures, write down the values of :
(i) sin x (ii) tan x (iii) sec x
(iv) cos y (v) cot y (vi) cosec y
(vii) sin z (viii) cos z (ix) tan z
Answer
View full question & answer→(i) $\frac{q}{r}$ (ii) $\frac{q}{p}$ (iii) $\frac{r}{p}$ (iv) $\frac{b}{n}$ (v) $\frac{b}{m}$ (vi) $\frac{n}{m}$ (vii) $\frac{u}{n}$ (viii) $\frac{k}{n}$ (ix) $\frac{u}{k}$
Question 195 Marks
Case Study II : In the figure given below, the rod AB of length 4 inches of a TV disc antena is fixed at right angle to the wall and a rod BC of length 8 inches is supporting the disc.
Based on the above information, answer the following questions:
1. The measure of $\angle$ACB is :
(a) $30^{\circ}$ (b) $45^{\circ}$
(c) $60^{\circ}$ (d) $90^{\circ}$
2. The value of tan $\angle$ABC is :
(a) $\frac{1}{\sqrt{3}}$ (b) $\sqrt{3}$
(c) 1 (d) 0
3. The value of $\sin ^2$ $\angle$ACB +$\sin ^2$ $\angle$ABC is :
(a) $\frac{1}{2}$ (b) 0 (c) 1 (d) not defined
4. The length of AC is :
(a) 6 inches (b) $5 \sqrt{3}$ inches (c) $4 \sqrt{2}$ inches (d) $4 \sqrt{3}$ inches
5. The value of sin $\angle$ACB +cos $\angle$ABC+cot $\angle$BAC is :
(a) 0 (b) 1 (c) 2 (d) not defined
Answer
View full question & answer→Case Study II (1. a), (2. b), (3. c), (4. d), (5. b)
Question 205 Marks
Case Study I : 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 BC = $2 \sqrt{3}$ m and $\angle$B = $90^{\circ}$.
Based on the above information, answer the following questions :
1. The length of AC is :
(a) 4 m (b) $8 \sqrt{3}$ m (c) $5 \sqrt{3}$ m (d) $4 \sqrt{3}$ m
2. The measure of $\angle$A is:
(a) $30^{\circ}$ (b) $45^{\circ}$ (c) $60^{\circ}$ (d) $90^{\circ}$
3. The measure of $\angle$C is:
(a) $30^{\circ}$ (b) $45^{\circ}$ (c) $60^{\circ}$ (d) $90^{\circ}$
4. cos 2A is equal to:
(a) 1 (b) $\frac{1}{2}$ (c) $\frac{\sqrt{3}}{2}$ (d) $\sqrt{3}$
5. $2 \sin \left(\frac{C}{2}\right)$ is equal to:
(a) 1 (b) $\frac{1}{2}$ (c) $\sqrt{3}$ (d) $\frac{\sqrt{3}}{2}$
Answer
View full question & answer→Case Study I (1. d), (2. a), (3. c), (4. b), (5. a)