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The Sine Ratio

Part of the Right-Triangle Trigonometry section of Coddy's Trigonometry journey. Lesson 4 of 46.

$Two escalators at 30°, one 20 m long and one 40 m long, sharing the same angle$

Two escalators both rise at 30°. One is 20 m long and the other is 40 m long. They have the same shape. The long one is twice as long, so it lifts you twice as high.

So for one angle, the height divided by the length is always the same number. In a triangle, opposite divided by hypotenuse is the sine: $\sin\left(\theta\right) = \frac{opposite}{hypotenuse}$ . Like the tangent, it depends only on the angle.

Challenge

This escalator is 46 m long and rises at 30°. How high, x, does it lift you? Choose the ratio that uses the length and the height.

Then press Check.

Try it yourself

$Use the figure to find x$

Use the figure to find x

All lessons in Right-Triangle Trigonometry

1Measuring With an Angle

How Tall Is the Tree?Naming the Sides The Tangent Ratio

4Finding the Hypotenuse

The Unknown Below the Bar How Long Is the Kite String?A Leg Below the Bar Is the Answer Sensible?Recap: The Hypotenuse

7Elevation and Depression

Angle of Elevation Measuring From Eye Level Angle of Depression The Sun's Angle Two Triangles, One Height Recap: Looking Up and Down

2The Three Ratios

The Sine RatioThe Cosine Ratio Choosing the Ratio Recap: The Three Ratios

5Finding an Angle

Inverse Sine Inverse Cosine Inverse Tangent The Angle of a Ramp Both Acute Angles Recap: Finding an Angle

8Reciprocal Ratios

Cosecant, Secant, Cotangent Exact Reciprocal Values A Side From a Cosecant A Ladder and a Secant Recap: Reciprocal Ratios

3Finding a Side

Sides at Any Angle Rounding the Answer Tangent: Leg From Leg A Ladder Against a Wall The Other Acute Angle Recap: Finding a Side

6Special Triangles, Exactly

The Two Special Triangles An Exact Hypotenuse The Side Next to 30°An Exact Angle Recap: Exact Values

9Final Challenges

Is the Ladder Safe?The Wheelchair Ramp Two Observers The Landing Plane The Kite The Sun's Angle, Exactly