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All questions of Trigonometry for BMAT Exam

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Can you explain the answer of this question below:
If 7sin2x + 3cos2x = 4 then , secx + cosecx =
  • A:
  • B:
  • C:
  • D:
The answer is a.

Gunjan Lakhani answered
7sin2x+3cos2 x=4
7sin2x+3(1-sin2x)=4
7sin2x+3-3sin2x=4
4sin2x=4-3
4sin2x=1
sin2x=¼
sinx=½
Cosec x=1/sinx=2
Cos x= 
Sec x= 1/cos x= 
Cosec x + sec x=2+ 

 The value of tan1°.tan2°.tan3°………. tan89° is :
  • a)
    2
  • b)
    1
  • c)
    1/2
  • d)
    0
Correct answer is option 'B'. Can you explain this answer?

Meera Rana answered
tan 1.tan 2.tan 3...tan (90 - 3 ).tan ( 90 - 2 ).tan ( 90 - 1) 
=tan 1.tan 2 .tan 3...cot 3.cot 2.cot 1 
=tan 1.cot 1.tan 2.cot 2.tan 3.cot 3 ... tan 89.cot 89 
1 x 1 x 1 x 1 x ... x 1 =1

The value of     is
  • a)
    2
  • b)
    0
  • c)
    4
  • d)
    -2
Correct answer is option 'D'. Can you explain this answer?

Krishna Iyer answered
we know sin(90 - a) = cos(a) 
cos(90 - a) = sin(a)
sin(a) = 1/cosec(a)
sec(a) = 1/cos(a)
 
cos40 = cos(90-50) = sin50
cosec40 = cosec(90-50) = sec50
so our expression becomes
sin50/sin50 + sec50/sec50 - 4cos50 / sin40
= 1 + 1 - 4(1)   since cos50 = sin40
= -2

 If the length of a shadow cast by a pole is  √3  times the length of the pole, then the angle of elevation of the sun is​
  • a)
    45°
  • b)
    60°
  • c)
    30°
  • d)
    90°
Correct answer is option 'C'. Can you explain this answer?

Anjana Khatri answered

Consider the height of tower be h

∴ height of shadow =√3h .

In a triangle ABC, 

tan ∠ACB = h / √3h

tan ∠ACB = 1 / √3

∠ACB = 30degree.

Therefore, angle of elevation is 30degree .

 If the angle of elevation of a cloud from a point 60 metres above a lake is 30o and the angle of depression of its reflection in the lake is 60°, then the height of the cloud above the lake is​
  • a)
    30 m
  • b)
    120 m
  • c)
    200 m
  • d)
    500 m
Correct answer is option 'B'. Can you explain this answer?

Neha Patel answered
Let AB be the surface of the lake and P be the point of observation such that AP = 60 m. Let C be the position of the cloud and C be its reflection in the lake.
Then CB = 
Draw PM⊥CB
Let CM = h
∴ CB = h + 60 m

The value of cos θ cos(90° - θ) – sin θ sin (90° - θ) is:
  • a)
    1
  • b)
    0
  • c)
    -1
  • d)
    2
Correct answer is option 'B'. Can you explain this answer?

Vikas Kumar answered
Explanation:

- Given expression: cos θ cos(90° - θ) – sin θ sin (90° - θ)
- We know that cos(90° - θ) = sin θ and sin(90° - θ) = cos θ
- Substitute these values into the expression:
= cos θ * sin θ - sin θ * cos θ
= sin θ cos θ - sin θ cos θ
= 0
- Therefore, the value of the expression is 0.

 If A and B are the angles of a right angled triangle ABC, right angled at C, then 1+cot2A =​
  • a)
    cot2B
  • b)
    sec2B
  • c)
    cos2B
  • d)
    tan2B
Correct answer is option 'B'. Can you explain this answer?

Siddharth answered
ABC is a Δ, right angle at c.
1 +cot^2 =?........ 
we know that.....
Cosec^2 - cot^2= 1...
So,
=> 1+ cot^2
=> cosec^2 A
=> (AB)^2/( CB)^2 
= sec ^2B.

The value of cos2 17° – sin2 73° is
  • a)
    0
  • b)
    1
  • c)
    -1
  • d)
    3
Correct answer is 'A'. Can you explain this answer?

Amit Sharma answered
cos217-sin273
=cos217-sin2(90-17)
=cos217-cos217   (because sin(90-x)=cos x)
=0

 The angle of elevation of the sun, when the length of the shadow of a tree is equal to the height of the tree, is:
  • a)
    45°
  • b)
    60°
  • c)
    30°
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Ananya Das answered

Consider the diagram shown above where QR represents the tree and PQ represents its shadow
We have, QR = PQ
Let ∠QPR = θ
tan θ = QR/PQ = 1 (since QR = PQ)
⇒ θ = 45°
i,e., required angle of elevation = 45°

A tower stands vertically on the ground. From a point on the ground which is 25 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 45o. Then the height (in meters) of the tower is​
  • a)
    25
  • b)
    25√3
  • c)
    12.5
  • d)
    25√2
Correct answer is option 'A'. Can you explain this answer?

Vikram Kapoor answered

A point on the ground which is 25 m away from the foot of the tower i. BC= 25 m
Let the height of the tower be x
The angle of elevation of the tower is found to be 45 degree.i.e.∠ACB=45°
In ΔABC
Using trigonometric ratios

Hence the height of the tower is 25 m.

The angle of elevation from a point 30 metre from the base of tree as level ground to the top of the tree is 60°. The height of the tree is : 
  • a)
    60√3 m
  • b)
    30√3 m
  • c)
    30 m
  • d)
    30/√3 m
Correct answer is option 'B'. Can you explain this answer?

Krishna Iyer answered
Angle of elevation is 60
Base = 30m
Height of the tree = Perpendicular
So in the right triangle
Where base is given and we have to find perpendicular we have only tan θ
So, Tan θ = P/B
Tan 60 = P/30
√30 = P/30
P = 30√30

Tree is broken by the wind the top struck the ground at 30° at a distance of 30m. away from the root. Find the height of the tree.
  • a)
    45.9
  • b)
    88.60
  • c)
    54.63
  • d)
     51.96
Correct answer is option 'D'. Can you explain this answer?

Neha Patel answered
let , 
the height of standing part of the tree be = h 
the height of  fallen part (forms hypotenuse) be = x
then the total height of the tree will be = h + x 
now, 
tan 30 = h/30 m
     1/√3 = h/30 m 
    30/√3 = h
    ⇒ h= 30/√3 m           .... 1
similarly, 
cos 30 = 30 m/ x 
   √3/2 = 30 / x
√3x = (30)2 
 √3x = 60 m 
⇒ x = 60 / √3 m           ....2
       ( we now have both value of h and x )
   on adding equation1 & 2 :
 ⇒ h + x = 30 /√3 +60 /√3
         =90 /√3 m 
         = 60√3 m
so , the total height of the tree is 60√3 m .

A tree casts a shadow 4 m long on the ground, when the angle of elevation of the sun is 45o. The height of the tree is:​
  • a)
    5.2 m
  • b)
    4 m
  • c)
    3 m
  • d)
    4.5 m
Correct answer is option 'B'. Can you explain this answer?

Nisha Choudhury answered
In a triangle with one angle being 90 degrees (which the tree makes with the ground) and the other being 45 degrees (the angle of elevation), the 3rd angle is bound to be 45 degrees (180 - 90 - 45 = 45). 

We also know that sides opposite to equal angles are equal.

Hence, the height of the tree will also be 4m.

An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from his eyes is 45°. The height of the tower is​
  • a)
    10 m
  • b)
    40 m
  • c)
    30 m
  • d)
    20 m
Correct answer is option 'C'. Can you explain this answer?

EduRev Class 10 answered
To solve for the height of the tower, we use the tangent function. The angle of elevation is 45°, and the horizontal distance from the observer to the tower is 28.5 m.
Let the height of the tower be h. The observer's eye level is 1.5 m, so the difference in height between the top of the tower and the observer's eyes is h−1.5h.

A tree is broken by wind and its upper part touches the ground at a point 10 metres from the foot of the tree and makes an angle of 45° with the ground. The entire length of the tree is​
  • a)
    20 m
  • b)
    10(1+√2)m
  • c)
    10 m
  • d)
    10√2 m
Correct answer is option 'B'. Can you explain this answer?

Drishti Kumari answered
Base = 10m
Angle of elevation = 45 degree
tan 45 ^ = P / b ( Let p supoose h )
1= h / 10
h = 10 m
height of half tree = 10 m
Now the length of broken part i.e, hypotenuse
H^2 = P ^2 + B ^2
H ^2 = 10^2 + 10 ^2
H ^2 = 100 +100
H = root under 100
H = 10 root 2

Hence , the length of entire tree = 10 + 10 root2
10 ( 1 + root 2 )
That's why B is the correct optipn .

 If the angles of depression from the top of a tower of height 40 m to the top and bottom of a tree are 45° and 60° respectively, then the height of the tree is
  • a)
  • b)
  • c)
  • d)
    None of the above
Correct answer is option 'B'. Can you explain this answer?

EduRev Class 10 answered
A tower of height 40 m is given, and the angles of depression from the top of the tower to:
  • The top of the tree = 45°
  • The bottom of the tree = 60°
We need to find the height of the tree (h).
Step 1: Use trigonometry for the angles of depression
Let:
  • The distance between the base of the tower and the base of the tree = d
  • The height of the tree = h
From the 45° angle (to the top of the tree):
The formula is:
tan(45°) = (Height of the tower - Height of the tree) / Distance (d)
Since tan(45°) = 1:
1 = (40 - h) / d
d = 40 - h (1)
From the 60° angle (to the bottom of the tree):
The formula is:
tan(60°) = Height of the tower / Distance (d)
Since tan(60°) = √3:
√3 = 40 / d
d = 40 / √3 (2)
Step 2: Solve the equations
Equate d from equations (1) and (2):
40 - h = 40 / √3
Rearrange to solve for h:
h = 40 - (40 / √3)
Rationalize the denominator:
h = 40 - (40√3 / 3)
h = (120 / 3) - (40√3 / 3)
h = (40 (3 - √3)) / 3
The height of the tree is:
b) (40 / 3) (3 - √3)

If 7sin2x + 3cos2x = 4 then , secx + cosecx =
  • a)
  • b)
  • c)
  • d)
Correct answer is 'A'. Can you explain this answer?

Naina Sharma answered
7sin2x+3cos2 x=4
7sin2x+3(1-sin2x)=4
7sin2x+3-3sin2x=4
4sin2x=4-3
4sin2x=1
sin2x=¼
sinx=½
Cosec x=1/sinx=2
Cos x= 
Sec x= 1/cos x= 
Cosec x + sec x=2+ 

The angle of elevation from a point 30 feet from the base of a pole, of height h, as level ground to the top of the pole is 45o. Which equation can be used to find the height of the pole.
  • a)
    cos 45° = h/30
  • b)
    tan 45° = 30/h
  • c)
    tan 45° = h/30
  • d)
    sin 45° = h/30
Correct answer is option 'C'. Can you explain this answer?

Prabhat jha answered
= h/30
b)sin 45 = h/30
c)tan 45 = h/30
d)sec 45 = h/30

Answer: b) sin 45 = h/30

Explanation:
The angle of elevation is the angle between the horizontal ground and the line of sight to the top of the pole. In this case, the angle of elevation is 45 degrees.

We can use the trigonometric ratio of sine to find the height of the pole. The sine of an angle is the ratio of the opposite side to the hypotenuse in a right triangle.

In this case, the opposite side is the height of the pole (h) and the hypotenuse is the distance from the point to the base of the pole (30 feet). Therefore, we have:

sin 45 = h/30

Solving for h, we get:

h = 30 sin 45

Using a calculator, we find that sin 45 is approximately 0.707. Therefore,

h = 30 x 0.707 = 21.21 feet

So the height of the pole is approximately 21.21 feet.

चित्तियों वाले केलों की क्या विशेषता होती हैं?
  • a)
    वे सुपाच्य होते हैं
  • b)
    वे सस्ते होते हैं
  • c)
    वे अधिक दिन तक नहीं रह सकते
  • d)
    वे गर्मियों में ही मिलते हैं
Correct answer is option 'A'. Can you explain this answer?

Nilanjan Unni answered
This question is incomplete as it does not provide any context or information to make a proper answer choice. Without any additional information, it is not possible to determine the correct answer for this question.

It is important to provide sufficient details or a complete question in order to accurately answer it. Please provide more information or context so that I can assist you better.

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