The acute angles in a right triangle are θ
and ϕ
. If sinϕ=0.25
, what is cosθ
?
Since the sum of angles in a triangle is always 180 degrees, we have:
θ + ϕ + 90 = 180
θ + ϕ = 90
Given that sin(ϕ) = 0.25, we can use the Pythagorean identity sin^2(x) + cos^2(x) = 1:
sin^2(ϕ) + cos^2(ϕ) = 1
0.25^2 + cos^2(ϕ) = 1
0.0625 + cos^2(ϕ) = 1
cos^2(ϕ) = 1 - 0.0625
cos^2(ϕ) = 0.9375
cos(ϕ) = √0.9375
cos(ϕ) = 0.9682
Since θ + ϕ = 90, we can substitute the value of cos(ϕ) into the equation:
cos(θ) = sin(90 - ϕ)
cos(θ) = sin(90)cos(ϕ) - cos(90)sin(ϕ)
cos(θ) = 1 x 0.9682 - 0 x 0.25
cos(θ) = 0.9682
Therefore, cos(θ) = 0.9682.