Advertisements
Advertisements
प्रश्न
In ∆ABC, if ∠A = 30°, ∠B = 60°, then the ratio of sides is ______.
विकल्प
`1 : sqrt(3) : 2`
`2 : sqrt(3) : 1`
`sqrt(3) : 1 : 2`
`sqrt(3) : 2 : 1`
Advertisements
उत्तर
In ∆ABC, if ∠A = 30°, ∠B = 60°, then the ratio of sides is `bbunderline(1 : sqrt(3) : 2)`.
Explanation:
Let us assume the length of the side opposite to ∠B = x.
In ΔABC, we have
sin(∠B) = sin 30° = `x/(AB)`
⇒ `1/2 = x/(AB)`
⇒ AB = 2x ...(i)
And, tan 30° = `x/(BC)`
⇒ `1/sqrt3 = x/(BC)`
⇒ BC = `sqrt3x` ...(ii)
∴ AC : BC : AB = x : x√3 : 2x
= 1 : √3 : 2
संबंधित प्रश्न
In Δ ABC with the usual notations prove that `(a-b)^2 cos^2(C/2)+(a+b)^2sin^2(C/2)=c^2`
In a Δ ABC, with usual notations prove that:` (a -bcos C) /(b -a cos C )= cos B/ cos A`
In any ΔABC, with usual notations, prove that b2 = c2 + a2 – 2ca cos B.
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`
With usual notations, in ΔABC, prove that a(b cos C − c cos B) = b2 − c2
The principal solutions of cot x = -`sqrt3` are .................
In , ΔABC prove that
`"sin"(("B" - "C")/2) = (("b" - "c")/"a") "cos"("A"/2)`
Find the polar co-ordinates of the point whose Cartesian co-ordinates are.
`(sqrt(2), sqrt(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 ΔABC, prove the following:
`("c" - "b cos A")/("b" - "c cos A") = ("cos B")/("cos C")`
In ΔABC, if `"cos A"/"a" = "cos B"/"b"`, then show that it is an isosceles triangle.
In Δ ABC, if a cos2 `"C"/2 + "c cos"^2 "A"/2 = "3b"/2`, then prove that a, b, c are in A.P.
State whether the following equation has a solution or not?
cos 2θ = `1/3`
If polar co-ordinates of a point are `(3/4, (3pi)/4)`, then its Cartesian co-ordinate are ______
In ∆ABC, if sin2A + sin2B = sin2C, then show that a2 + b2 = c2
Find the polar co-ordinates of point whose Cartesian co-ordinates are `(1, sqrt(3))`
In ∆ABC, prove that `("b" - "c")^2 cos^2 ("A"/2) + ("b" + "c")^2 sin^2 ("A"/2)` = a2
In ΔABC, if a cos A = b cos B, then prove that ΔABC is either a right angled or an isosceles triangle.
In ∆ABC, prove that `(cos 2"A")/"a"^2 - (cos 2"c")/"c"^2 = 1/"a"^2 - 1/"c"^2`
In ∆ABC, prove that `(cos^2"A" - cos^2"B")/("a" + "b") + (cos^2"B" - cos^2"C")/("b" + "c") + (cos^2"C" - cos^2"A")/("c" + "a")` = 0
In ΔABC, prove that `("a"^2sin("B" - "C"))/(sin"A") + ("b"^2sin("C" - "A"))/(sin"B") + ("c"^2sin("A" - "B"))/(sin"C")` = 0
In ∆ABC, if ∠A = `pi/2`, then prove that sin(B − C) = `("b"^2 - "c"^2)/("b"^2 + "c"^2)`
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 ________.
In ΔABC, `(sin(B - C))/(sin(B + C))` = ______
In Δ ABC, with the usual notations, if `(tan "A"/2)(tan "B"/2) = 3/4` then a + b = ______.
In ΔABC if sin2A + sin2B = sin2C and l(AB) = 10, then the maximum value of the area of ΔABC is ______
In ΔABC, a = 7cm, b = 3cm and c = 8 cm, then angle A is ______
In any triangle ABC, the simplified form of `(cos2A)/a^2 - (cos2B)/b^2` is ______
If in Δ ABC, 3a = b + c, then `cot ("B"/2) cot ("C"/2)` = ______.
If in ΔABC, `sin "B"/2 sin "C"/2 = sin "A"/2` and 2s is the perimeter of the triangle, then s is ______.
In a triangle ABC, b = `sqrt3`, c = 1 and ∠A = 30°, then the largest angle of the triangle is ______
If a = 13, b = 14, c = 15, then `cos("A"/2)` = ______.
In a ΔABC, if a = `sqrt(2)` x and b = 2y and ∠C = 135°, then the area of triangle is ______.
If in a triangle ABC, AB = 5 units, AB = 5 units, ∠B = `cos^-1 (3/5)` and radius of circumcircle of ΔABC is 5 units, then the area (in sq.units) of ΔABC is ______.
In triangle ABC, a = 4, b = 3 and ∠A = 60°. If ' c' is a root of the equation c2 – 3c – k = 0. Then k = ______. (with usual notations)
In a triangle ABC, in usual notation, (a + b + c)(b + c – a) = λbc will be true if ______.
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 any ΔABC, prove that:
(b + c) cos A + (c + a) cos B + (a + b) cos C = a + b + c.
If in ΔABC, `sin A/2 * sin C/2 = sin B/2` and 2s is the perimeter of the triangle, then s = ______.
In ΔABC, a = 3, b = 1, cos(A – B) = `2/9`, find 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 =
