English

In ΔABC, a = 3, b = 4 and sin A = 34, find ∠B

Advertisements
Advertisements

Question

In ΔABC, a = 3, b = 4 and sin A = `3/4`, find ∠B

Sum
Advertisements

Solution

By sine rule,

`"a"/(sin "A") = "b"/(sin "B")`

∴ `3/(3/4) = 4/(sin "B")`

∴ sin B = 1 = `sin  pi/2`

∴ ∠B = `pi/2`

shaalaa.com
  Is there an error in this question or solution?
Chapter 1.3: Trigonometric Functions - Very Short Answers

APPEARS IN

RELATED QUESTIONS

In any ΔABC if  a2 , b2 , c2 are in arithmetic progression, then prove that Cot A, Cot B, Cot C are in arithmetic progression.


In Δ ABC, if a = 13, b = 14 and c = 15, then sin (A/2)= _______.

(A) `1/5`

(B) `sqrt(1/5)`

(C) `4/5`

(D) `2/5`


 In , ΔABC with usual notations prove that

(a-b)2 cos2 `("C"/2) +("a"+"b")^2 "sin"^2("C"/2) = "c"^2`


Find the Cartesian co-ordinates of the point whose polar co-ordinates are:

`(1/2, (7pi)/3)`


Find the polar co-ordinates of the point whose Cartesian co-ordinates are.

`(0, 1/2)`


Find the polar coordinates of the point whose Cartesian coordinates are `(1, - sqrt(3))`.


Find the polar co-ordinates of the point whose Cartesian co-ordinates are.

`(3/2, (3√3)/2)`.


In ΔABC, if cot A, cot B, cot C are in A.P. then show that a2, b2, c2 are also in A.P.


In any Δ ABC, prove the following:

a2 sin (B - C) = (b2 - c2) sin A.


Prove that `tan^-1 sqrt"x" = 1/2 cos^-1 ((1 - "x")/(1 + "x"))`, if x ∈ [0, 1]


Show that `(9pi)/8 - 9/4 sin^-1 (1/3) = 9/4 sin^-1 ((2sqrt2)/3)`.


In ∆ABC, if ∠A = 30°, ∠B = 60°, then the ratio of sides is ______.


In ∆ABC, if b2 + c2 − a2 = bc, then ∠A = ______.


In ∆ABC, prove that ac cos B − bc cos A = a2 − b2 


In ∆ABC, if sin2A + sin2B = sin2C, then show that a2 + b2 = c2 


Find the Cartesian co-ordinates of point whose polar co-ordinates are `(4, pi/3)`


In ∆ABC, prove that `("b" - "c")^2 cos^2 ("A"/2) + ("b" + "c")^2 sin^2 ("A"/2)` = a2 


In ∆ABC, if a = 13, b = 14, c = 15, then find the value of cos B


In ∆ABC, prove that `(cos 2"A")/"a"^2 - (cos 2"c")/"c"^2 = 1/"a"^2 - 1/"c"^2`


In ΔABC, prove that `("b"^2 - "c"^2)/"a" cos"A" + ("c"^2 - "a"^2)/"b" cos"B" + ("a"^2 - "b"^2)/"c" cos "C"` = 0


In ΔABC, if (a+ b - c)(a + b + c) = 3ab, then ______.


In a triangle ABC, If `(sin "A" - sin "C")/(cos "C" - cos "A")` = cot B, then A, B, C are in ________.


If one side of a triangle is double the other and the angles opposite to these sides differ by 60°, then the triangle is ______


If `(- sqrt2, sqrt2)` are cartesian co-ordinates of the point, then its polar co-ordinates are ______.


In ΔABC, `(sin(B - C))/(sin(B + C))` = ______


If cartesian co-ordinates of a point are `(1, -sqrt3)`, then its polar co-ordinates are ______ 


The smallest angle of the ΔABC, when a = 7, b = `4sqrt(3)` and c = `sqrt(13)` is ______.


If polar co-ordinates of a point are `(1/2, pi/2)`, then its cartesian co-ordinates are ______.


In ΔABC, `cos"A"/"a" = cos"B"/"b"  cos"C"/"c"`. If a = `1/sqrt(6)`, then the area of the triangle is ______.


In a ΔABC, if `sin"A"/sin"C" = (sin("A" - "B"))/(sin("B" - "C"))`, then a2, b2, c2 are in ______.


In a ΔABC, if a = `sqrt(2)` x and b = 2y and ∠C = 135°, then the area of triangle is ______.


In ΔABC with usual notations, if ∠A = 30° and a = 5, then `s/(sumsinA)` is equal to ______.


Let ABC be a triangle such that ∠A = 45°, ∠B = 75° then `"a" + "c"sqrt(2)` is equal to ______. (in usual notation)


In ΔABC, with usual notations, if a, b, c are in A.P. Then `a cos^2 (C/2) + c cos^2(A/2)` = ______.


In ΔABC, `(a - b)^2 cos^2  C/2 + (a + b)^2 sin^2  C/2` is equal to ______.


In any ΔABC, prove that:

(b + c) cos A + (c + a) cos B + (a + b) cos C = a + b + c.


In a triangle ABC, with usual notations, if \[\frac{2\cos\mathrm{A}}{\mathrm{a}}+\frac{\cos\mathrm{B}}{\mathrm{b}}+\frac{2\cos\mathrm{C}}{\mathrm{c}}=\frac{\mathrm{a}}{\mathrm{bc}}+\frac{\mathrm{b}}{\mathrm{ac}}\]then ∠A =


In a triangle ABC with usual notations, if a,b, and c are in arithmetic progression, then, \[\tan\frac{A}{2}\cdot\tan\frac{C}{2}=\]


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×