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How Tall Is the Tree?

Part of the Right-Triangle Trigonometry section of Coddy's Trigonometry journey. Lesson 1 of 46.

The tree is too tall to climb. Its shadow is 20 m long. The sun's ray rises at 37° from the tip of the shadow. How tall is the tree?

$A tree of height h, its 20 m shadow, and the sun's ray rising at 37° from the tip of the shadow$

For every metre of ground, the ray climbs the same amount. That amount is the tangent of the angle, $\tan\left(37^{\circ}\right)$ . So the tree is 20 × $\tan\left(37^{\circ}\right)$ metres tall.

Challenge

Find the height h of the tree. The board starts with the tangent ratio for this triangle: tan(37°) = h/20. Get h alone and round it. Done means h is a number of metres with 2 decimals.

Then press Check.

Try it yourself

$Use the figure to find h$

\tan 37^{\circ} = \frac{h}{20}

Use the figure to find h

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 Ratio The 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