Advertisements
Advertisements
Question
In ΔABC, if a = 18, b = 24, c = 30 then find the values of A(ΔABC)
Solution
Given: a = 18, b = 24 and c = 30
∴ 2s = a + b + c
= 18 + 24 + 30
= 72
∴ s = 36
`A(ΔABC) = sqrt(s(s - a)(s - b)(s - c)`
`= sqrt(36(36 - 18)(36 - 24)(36 - 30)`
`= sqrt(36 xx 18 xx 12 xx 6)`
`= sqrt(36 xx 18 xx 4 xx 18)`
= 6 x 18 x 2
= 216 sq units.
APPEARS IN
RELATED QUESTIONS
Show that `2sin^-1(3/5) = tan^-1(24/7)`
Find the principal values of `sin^(-1) (-1/2)`
Find the principal value of `tan^(-1) (-sqrt3)`
Find the principal value of `sec^(-1) (2/sqrt(3))`
Find the principal value of `cos^(-1) (-1/sqrt2)`
Find the principal value of `cosec^(-1)(-sqrt2)`
Find the value of the following:
If sin−1 x = y, then
Find the principal value of `sin^-1(1/sqrt2)`
`sin^-1 1/2-2sin^-1 1/sqrt2`
`sin^-1{cos(sin^-1 sqrt3/2)}`
Find the domain of the following function:
`f(x)=sin^-1x+sin^-1 2x`
Evaluate the following:
`tan^-1 1+cos^-1 (-1/2)+sin^-1(-1/2)`
Evaluate the following:
`tan^-1(tan (5pi)/6)+cos^-1{cos((13pi)/6)}`
Find the domain of `f(x)=cotx+cot^-1x`
Solve for x:
`tan^-1 [(x-1),(x-2)] + tan^-1 [(x+1),(x+2)] = x/4`
In ΔABC, if a = 18, b = 24, c = 30 then find the values of cosA
In ΔABC, if a = 18, b = 24, c = 30 then find the values of cos `A/2`
Find the principal value of the following: cosec- 1(2)
Evaluate the following:
`tan^-1(1) + cos^-1(1/2) + sin^-1(1/2)`
Prove the following:
`tan^-1["cosθ + sinθ"/"cosθ - sinθ"] = pi/(4) + θ, if θ ∈ (- pi/4, pi/4)`
In ΔABC, prove the following:
`(cos A)/a + (cos B)/b + (cos C)/c = (a^2 + b^2 + c^2)/(2abc)`
The principal value of sin−1`(1/2)` is ______
`tan^-1(tan (7pi)/6)` = ______
Prove that `2 tan^-1 (3/4) = tan^-1(24/7)`
If tan−1x + tan−1y + tan−1z = π, then show that `1/(xy) + 1/(yz) + 1/(zx)` = 1
Prove that cot−1(7) + 2 cot−1(3) = `pi/4`
Prove that:
2 tan-1 (x) = `sin^-1 ((2x)/(1 + x^2))`
Solve `tan^-1 2x + tan^-1 3x = pi/4`
Evaluate:
`cos[tan^-1 (3/4)]`
Find the principal value of `sin^-1 1/sqrt(2)`
Find the principal value of `cos^-1 sqrt(3)/2`
Choose the correct alternative:
cos 2θ cos 2ϕ+ sin2 (θ – ϕ) – sin2 (θ + ϕ) is equal to
`sin^-1x + sin^-1 1/x + cos^-1x + cos^-1 1/x` = ______
lf `sqrt3costheta + sintheta = sqrt2`, then the general value of θ is ______
sin[3 sin-1 (0.4)] = ______.
If `sin^-1x + cos^-1y = (3pi)/10,` then `cos^-1x + sin^-1y =` ______
The principal value of `tan^{-1(sqrt3)}` is ______
In a triangle ABC, ∠C = 90°, then the value of `tan^-1 ("a"/("b + c")) + tan^-1("b"/("c + a"))` is ______.
If `tan^-1x + tan^-1y = (4pi)/5`, then `cot^-1x + cot^-1y` equals ______.
`(sin^-1(-1/2) + tan^-1(-1/sqrt(3)))/(sec^-1 (-2/sqrt(3)) + cos^-1(1/sqrt(2))` = ______.
`cos^-1 4/5 + tan^-1 3/5` = ______.
If `3tan^-1x +cot^-1x = pi`, then xis equal to ______.
The domain of the function y = sin–1 (– x2) is ______.
Solve the following equation `cos(tan^-1x) = sin(cot^-1 3/4)`
Prove that `tan^-1 1/4 + tan^-1 2/9 = sin^-1 1/sqrt(5)`
All trigonometric functions have inverse over their respective domains.
When `"x" = "x"/2`, then tan x is ____________.
If `"cos"^-1 "x + sin"^-1 "x" = pi`, then the value of x is ____________.
`"sin"^-1 (-1/2)`
If 6sin-1 (x2 – 6x + 8.5) = `pi`, then x is equal to ____________.
`2 "tan"^-1 ("cos x") = "tan"^-1 (2 "cosec x")`
If `"x" in (- pi/2, pi/2), "then the value of tan"^-1 ("tan x"/4) + "tan"^-1 ((3 "sin" 2 "x")/(5 + 3 "cos" 2 "x"))` is ____________.
`sin[π/3 - sin^-1 (-1/2)]` is equal to:
`"cos" ["tan"^-1 {"sin" ("cot"^-1 "x")}]` is equal to ____________.
The number of solutions of sin–1x + sin–1(1 – x) = cos–1x is
The inverse of `f(x) = sqrt(3x^2 - 4x + 5)` is
Domain and Rariges of cos–1 is:-
What will be the principal value of `sin^-1(-1/2)`?
What is the principal value of cosec–1(2).
Find the value, if sin–1x = y, then `->`:-
Value of `sin(pi/3 - sin^1 (- 1/2))` is equal to
If f'(x) = x–1, then find f(x)
Assertion (A): The domain of the function sec–12x is `(-∞, - 1/2] ∪ pi/2, ∞)`
Reason (R): sec–1(–2) = `- pi/4`
Number of values of x satisfying the system of equations `sin^-1sqrt(2 + e^(-2x) - 2e^-x) + sec^-1sqrt(1 - x^2 + x^4) = π/2` and `5^(1+tan^-1x)` = 4 + [cos–1x] is ______ (where [.] denotes greatest integer function)
cos–1(cos10) is equal to ______.
Number of values of x which lie in [0, 2π] and satisfy the equation
`(cos x/4 - 2sinx) sinx + (1 + sin x/4 - 2cosx)cosx` = 0
The value of cos (2cos–1 x + sin–1 x) at x = `1/5` is ______.
`(tan^-1 (sqrt(3)) - sec^-1(-2))/("cosec"^-1(-sqrt(2)) + cos^-1(-1/2))` is equal to ______.
sin [cot–1 (cos (tan–1 x))] = ______.
If tan 4θ = `tan(2/θ)`, then the general value of θ is ______.
