Step-by-step explanation:
Follow the Pic given above
Given: sin theta = 2/5. This tells us that the lengths of the opp side and the hyp are 2 and 5 respectively. The adj side is found using the Pyth. Thm.: 5^2-2^2= 25-4 = 21, so that the adj side is sqrt(21).
The double angle formula for the sine is sin 2theta = 2 sin theta *cos theta.
In this particular problem, the sine of 2theta is 2*(2/5)*[sqrt(21) / 5], or:
(4/25)*sqrt(21).
5/6 is your answer, explanation is in the image, hope this helps! :D
Answer:
See the attached figure which represents the problem.
As shown, AA₁ and BB₁ are the altitudes in acute △ABC.
△AA₁C is a right triangle at A₁
So, Cos x = adjacent/hypotenuse = A₁C/AC ⇒(1)
△BB₁C is a right triangle at B₁
So, Cos x = adjacent/hypotenuse = B₁C/BC ⇒(2)
From (1) and (2)
∴ A₁C/AC = B₁C/BC
using scissors method
∴ A₁C · BC = B₁C · AC