Trigonometry Test

Result

Trigonometry Test - 7

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Weekly Quiz Competition

Question 1
1 / -0

tan 1° tan 2° tan 3° …… tan 89° is equal to

A
0

B
not defined

C
1

D

Solution

tan 1^o tan 2^o tan 3^o ……. tan 88^o tan 89^o
= (tan 1^o tan 89^o) (tan 2^o tan 88^o) x (tan 3^o tan 87^o)…… (tan 45^o) [as tan (90^o - ) = cot ]
= (tan 1^o cot 1^o) (tan 2^o cot 2^o)…. (tan 45^o) = 1.1.1………1 = 1
Question 2
1 / -0

From a 60 metre high tower, angles of depression of the top and bottom of a house are and respectively. If the height of the house is, then x is equal to

A
sin sin

B
cos cos

C
sin cos

D
cos sin

Solution

H = d tan b and H - h = d tan a
As H = 60

h =
Question 3
1 / -0

Choose the right option if Psin³+Qcos³ = sin cos and P sin= Qcos.

A
P³ + Q³ = 1

B
P² – Q² = 1

C
P² + Q² = 1

D
None of these

Solution

P sin sin²+Qcos³ = sincos
Qcossin²+Qcos³ =sincos
Q = sin
P sin³+ Q cos.cos²=sincos
P sin³+ Q sin.cos²=sincos
P = cos
P² + Q² = 1
Question 4
1 / -0

The angle of depression of an object from a tower of height 150 m is 30⁰. The distance of object from tower is

A
50m

B
100m

C
150 m

D
none of these

Solution

tan A =
tan 30⁰ =
=
AB = 150m
Question 5
1 / -0

A ladder 24 m long is resting on the wall such that it touches the wall at midway of the wall's height. At the foot of the ladder, the angle of elevation from the midpoint of the wall is 45^o. Find the height of the wall.

A
24 m

B
18m

C
12 m

D
24 m

Solution

cosine 2 =
Cosine 45 =
x =
Question 6
1 / -0

If tan² = 2tan² + 1, then cos 2 + sin² is equal to

A
0

B
2sin²

C
– cos²2

D
None of these

Solution

cos 2 + sin² = + sin² = + sin²
= + sin² = + sin² = sin² – sin² = 0
Question 7
1 / -0

An observer on the top of a tree finds the angle of depression of a car moving at constant speed towards the tree to be 30⁰. After 3 minutes this angle becomes 60⁰. After how much more time, the car will reach the tree?

A
4 min

B
4.5 min

C
1.5 min

D
None of these

Solution

d = h cot 30^o - h cot 60^o and time = 3 min.
Speed = per minute
It will travel distance
h cot 60^o in = 1.5 minutes.
Question 8
1 / -0

Choose the right option if x = a sin- b cos and Y= acos+b sin.

A

B

C
X²+Y² = a²+b²

D
None of these

Solution

By squaring and adding
Question 9
1 / -0

A ladder of 20 m long touches the wall at height of 10m. The angle made by it with the horizontal is

A
30⁰

B
60⁰

C
45⁰

D
90°

Solution

sin =
sin= =
= 30⁰
Question 10
1 / -0

A vertical pole is 300 m high. Find the angle subtended by its top at a point 300m from its base.

A
45°

B
30°

C
60°

D
37°

Solution

tan θ =
tan θ =
tan θ =
tan θ = tan
θ = 30°
Question 11
1 / -0

If tan = - , then sin =

A
- but not

B
- or

C
but not -

D
none of these

Solution

tan = - sec² = 1 + (-)²
sec² = 1 + Ãsec = Â±
cos = Â± .
Hence, sin = tancos = (-) (Â± ) = -.
Question 12
1 / -0

Two vertical poles of equal heights are 120 m apart. On the line joining their bottoms, A and B are two points. The angle of elevation of the top of one pole from A is 45^o and that of the other pole from B is also 45^o. If AB = 30 m, then the height of each pole is

A
40 m

B
45 m

C
50 m

D
42 m

Solution

tan 45^o = 1 = T₂ 'B = h
Also, tan 45^o = 1 = T₁ 'A = h

Hence, 120 m = h + 30 m + h h = 45 m
Question 13
1 / -0

If cos+ sin= 1 and sin- cos= 1, then

A
x²+ y² = a²+ b²

B

C
a²x²+ b²y²= 1

D
None of these

Solution
Question 14
1 / -0

The length of shadow of a tower is times that of its length. The angle of elevation of the sun is

A
45⁰

B
30⁰

C
60⁰

D
none of these

Solution

tan =
=
= 30⁰
Question 15
1 / -0

In a ABC, if and a = 2, the area of the triangle is:

A
1

B
2

C
/2

D

Solution

Sine formula,
-------(1)
-------(2)

Cot A = Cot B = Cot C

So, A = B = C
∠A = ∠B = ∠C = 60°
and ∠A + ∠B + ∠C = 180°
So, △ABC is an equilateral triangle
So, if a = 2, then a= b = c = 2
Area of △ABC = = =
Question 16
1 / -0

cos 1° cos 2° cos 3° …. cos 179° is equal to

A
positive real number

B
a negative real number

C
0

D
none of these

Solution

Now, cos 1° cos 2° cos 3° …. cos 179°

In the given expression, cos 90^o comes
cos 90° = 0

So, cos 1° cos 2° cos 3° …. cos 179° = 0
Question 17
1 / -0

The angles of elevation of a cliff at a point A on the ground and a point B 100m vertically above A are and respectively. The height of the cliff is

A

B

C

D

Solution

Let AD be the building of height 100 and BP be the hill. Then
tan = and tan =
tan = x cot = (100 + x) cot
x = 100 + x = 100 +
Question 18
1 / -0

If sin= and tan= , which of the following is correct?

A

B

C

D
None of these

Solution

We get this answer by squaring and subtracting.
Question 19
1 / -0

A person walking 20 m towards a chimney in a horizontal line through its base observes that its angle of elevation changes from 30^o to 45^o. The height of chimney is

A

B

C
20(

D
None of these

Solution

h =
=
=
=
Question 20
1 / -0

A pole 50 m high stands on a building 250 m high. To an observer at a height of 300 m, the building and the pole subtend equal angles. The distance of the observer from the top of the pole is

A
25 m

B
50 m

C
25 m

D
25m

Solution

= tan 45^o = 1