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A Ladder Against a Wall

Part of the Right-Triangle Trigonometry section of Coddy's Trigonometry journey. Lesson 15 of 50.

A ladder against a wall makes a right triangle: the wall and the ground meet at the right angle, and the ladder is the hypotenuse. Safety guides ask for about 75° between the ladder and the ground.

$A 5 m ladder against a wall at 70° to the ground, its foot d from the wall$

A 5 m ladder stands at 70°. How far is its foot from the wall? That distance d touches the 70° angle at the foot, so it is adjacent, and the ladder is the hypotenuse: cos(70°) = d/5, so d = 5cos(70°), about 1.71 m. The height it reaches is opposite 70°, so it needs the sine instead.

Challenge

A 6 m ladder leans against a wall and makes a 72° angle with the ground. How high up the wall does it reach? Find h to two decimal places. Then press Check.

Try it yourself

$Use the figure to find h$

Use the figure to find h

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 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 LegA Ladder Against a WallThe 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