The Sine Ratio
Part of the Right-Triangle Trigonometry section of Coddy's Trigonometry journey. Lesson 7 of 50.
Take a right triangle with an acute angle θ and divide the side opposite θ by the hypotenuse. That number is the sine of θ, written sin(theta).
sin θ = opposite / hypotenuse
In this 3, 4, 5 triangle, sin(theta) = 3/5. Draw the same angle in a triangle twice as big, with sides 6, 8 and 10, and the sine is 6/10, which is again 3/5. The size of the triangle does not matter, only the angle, so every angle has one sine. For a few angles the value is a simple number: sin(30°) = 1/2.
On the board, tap the angle and the two sides you want, then pick Sine ratio. The board writes the equation in the figure's own labels, and you solve it.
Challenge
Triangle PQR has a right angle at P and a 30° angle at Q. The hypotenuse is 14. Find the side x opposite the 30° angle: tap 30°, x and 14, pick Sine ratio, and solve. Then press Check.
Try it yourself
Use the figure to find x
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Right-Triangle Trigonometry
1Sides of a Right Triangle
How Tall Is the Tree?The HypotenuseThe Opposite SideThe Adjacent SideWhen the Angle MovesRecap: Naming the Sides2The Three Ratios
The Sine RatioThe Cosine RatioThe Tangent RatioChoosing the RatioRecap: The Three Ratios