Trigonometry

If $\sin θ = \frac{5}{13}$ , then $\cos θ$ is:
1. $\frac{12}{5}$
2. $\frac{13}{12}$
3. $\frac{12}{13}$
4. $\frac{\sqrt{5}}{13}$
If $4 \tan θ = 3$ , then $\frac{4 \sin θ - \cos θ}{4 \sin θ + \cos θ}$ is equal to:
1. $\frac{1}{2}$
2. $\frac{2}{3}$
3. $\frac{1}{3}$
4. $\frac{3}{4}$
From a point on the ground, 30 m away from the foot of a tower, the angle of elevation of the top of the tower is $30 °$ . The height of the tower is:
1. $30 \sqrt{3}$ m
2. 30 m
3. 10 m
4. $10 \sqrt{3}$ m
From a point on the ground which is 15m away from the foot of a tower, the angle of elevation is found to be $60 °$ . The height of the tower is:
1. $20 \sqrt{3}$ m
2. $15 \sqrt{3}$ m
3. 10 m
4. $10 \sqrt{3}$ m
If $\cot θ = \frac{7}{8}$ , then the value of $\frac{(1 + \sin θ) (1 - \sin θ)}{(1 + \cos θ) (1 - \cos θ)}$ is:
1. $\frac{49}{64}$
2. $\frac{8}{7}$
3. $\frac{64}{49}$
4. $\frac{7}{8}$
In right triangle ABC, right angled at C, if $\tan A = 1$ , then the value of $2 \sin A \cos A$ is:
1. 1
2. 2
3. 0
4. - 1
From a point P on the level ground, the angle of elevation of the top of a tower is $30 °$ . If the tower is 100m high, the distance between P and the foot of the tower is:
1. $100 \sqrt{3}$ m
2. $150 \sqrt{3}$
3. $300 \sqrt{3}$
4. $200 \sqrt{3}$
If the angle of depression of an object from a 75m high tower is $30 °$ , then the distance of the object from the tower is:
1. $25 \sqrt{3}$
2. $75 \sqrt{3}$
3. $50 \sqrt{3}$
4. $100 \sqrt{3}$
In $∆ A B C$ , if $∠ B = 90 °$ and $\cot A = 1$ , then the value of $\cos C \sin A - \cos A \sin C$ is:
1. 1
2. 2
3. - 1
4. 0
A ladder 14 m long rests against a wall. If the foot of the ladder is 7 m from the wall, then the angle of elevation is:
1. $30 °$
2. $75 °$
3. $60 °$
4. $45 °$
If the length of the shadow of a tower is $\sqrt{3}$ times that of its height, then the angle of elevation of the sun is:
1. $75 °$
2. $45 °$
3. $30 °$
4. $60 °$
If $\sin A = \frac{12}{13}$ , then $\tan A$ = ?
1. $\frac{13}{5}$
2. $\frac{5}{12}$
3. $\frac{12}{5}$
4. $\frac{13}{12}$
If $\tan θ = \frac{20}{21}$ , then $\frac{\cos θ - \sin θ}{\cos θ + \sin θ}$ is:
1. $\frac{1}{21}$
2. $\frac{21}{20}$
3. $\frac{1}{41}$
4. $\frac{1}{20}$
If $5 \tan α = 4$ , then the value of $\frac{5 \sin α - 3 \cos α}{5 \sin α + 2 \cos α}$ is:
1. $\frac{1}{6}$
2. $\frac{1}{5}$
3. $\frac{4}{5}$
4. $\frac{1}{4}$
In a $∆ A B C$ right angled at $∠ A = 30 °$ and AC = 6 cm, then the length of BC is:
1. 3 cm
2. $3 \sqrt{3}$ cm
3. $4 \sqrt{3}$ cm
4. $2 \sqrt{3}$ cm
If a kite is flying at a height of $10 \sqrt{3} m$ from the level ground attached to a string inclined at $60 °$ to the horizontal then the length of the string is:
1. $60 \sqrt{3} m$
2. $40 \sqrt{3} m$
3. 20 m
4. $80 \sqrt{3} m$
If $\tan θ = \frac{a}{b}$ , then $\frac{\cos θ + \sin θ}{\cos θ - \sin θ}$ is:
1. $\frac{b - a}{b + a}$
2. $\frac{a - b}{a + b}$
3. $\frac{b + a}{b - a}$
4. None of these
The top of a broken tree has its top touching the ground at a distance of 10m from the bottom. If the angle made by the broken part with the ground is $30 °$ , then the length of the broken part is:
1. 20 m
2. $\frac{20}{\sqrt{3}} m$
3. $10 \sqrt{3} m$
4. $20 \sqrt{3} m$
An electric pole is $10 \sqrt{3} m$ high and its shadow is 10 m in length, then the angle of elevation of the sun is:
1. $30 °$
2. $15 °$
3. $60 °$
4. $45 °$
If $\tan θ = \frac{20}{21}$ , then $\frac{1 - \sin θ + \cos θ}{1 + \sin θ + \cos θ}$ is:
1. $\frac{5}{7}$
2. $\frac{6}{7}$
3. $\frac{4}{7}$
4. $\frac{3}{7}$
The maximum value of $\frac{1}{\sec θ}$ is:
1. 0
2. 3
3. 1
4. 2
A kite is flying at a height of 60 m from the level ground, attached to a string inclined at $30 °$ to the horizontal. The length of the string is:
1. 60 m
2. $60 \sqrt{3}$ m
3. $40 \sqrt{3}$ m
4. 120 m
A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. If the angle made by the rope with the ground level is $30 °$ , then the height of the pole is:
1. 20 m
2. $20 \sqrt{3}$ m
3. $10 \sqrt{3}$ m
4. 10 m
In triangle PQR, if PR + QR = 25 cm and PQ = 5cm. Then the value of $\sin P + \tan P$ is:
1. 1
2. 4
3. $\frac{216}{65}$
4. 3
If $θ$ is an acute angle and $\tan θ + \cot θ = 2$ , then the value of $\tan^{25} θ + \cot^{25} θ$ is:
1. None of these
2. 2
3. 1
4. 0
A river is 60 m wide. A tree of unknown height is on one bank. The angle of elevation of the top of the tree from the point exactly opposite to the foot of the tree, on the other bank, is $30 °$ . The height of the tree is:
1. $60 \sqrt{3} m$
2. $30 \sqrt{3} m$
3. $20 \sqrt{3} m$
4. $10 \sqrt{3} m$
If A, B and C are interior angles of a triangle ABC, then the value of $\tan (\frac{B + C}{2})$ is:
1. $\tan (\frac{A}{2})$
2. None of these
3. $\cot (\frac{A}{2})$
4. $\sin (\frac{A}{2})$
Which of the following is true:
1. $\cos A \sec A = 1$
2. $\cos A + \sin A = 1$
3. $\sin A \cot A = 1$
4. $\sin A + c o s e c A = 1$
A bridge across a river makes an angle of $45 °$ with the river bank. If the length of the bridge across the river is 200 m, then the breadth of the river is:
1. 100 m
2. 200 m
3. $200 \sqrt{2}$ m
4. $100 \sqrt{2}$ m
The upper part of a tree broken by the wind falls to the ground without being detached. The top of the broken part touches the ground at an angle of $30 °$ at a point 8m from the foot of the tree. The original height of the tree is:
1. $24 \sqrt{3}$ m
2. $8 \sqrt{3}$ m
3. 8 m
4. 24 m

Trigonometry

Quiz