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A Side From a Cosecant

Part of the Right-Triangle Trigonometry section of Coddy's Trigonometry journey. Lesson 42 of 50.

A reciprocal ratio can find a side directly. Since csc θ is hypotenuse over opposite, the hypotenuse is the opposite side times csc θ: one multiplication.

The side opposite 40° is 6 and you want the hypotenuse x. csc(40°) = x/6, so x = 6csc(40°), about 9.33. With the sine the same answer comes from x = 6/sin(40°): multiplying by csc is dividing by sin.

$Right triangle with a 40° angle, the opposite side 6 and the hypotenuse x$

Challenge

In a right triangle the side opposite a 32° angle is 9 and the hypotenuse is x, so csc(32°) = x/9. Solve for x and round it to two decimal places. Then press Check.

Try it yourself

csc(32°) = x/9

Solve for x

Test yourself

This 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 Hypotenuse The Opposite Side The Adjacent Side When the Angle Moves Recap: Naming the Sides

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 Ratio The Cosine Ratio The Tangent 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 ValuesA Side From a CosecantA 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