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Two Observers

Part of the Right-Triangle Trigonometry section of Coddy's Trigonometry journey. Lesson 47 of 50.

Two surveyors stand on opposite sides of a radio mast on level ground. The first, 50 m from its foot, measures the top at 35° above the horizontal. The second measures 22°, but has no tape. How tall is the mast, and how far is the second surveyor from it?

Challenge

Use the figure: P is 50 m from the foot of the mast and sees the top at 35°, Q is on the other side and sees it at 22°. Find the mast's height h and Q's distance x from it, both to two decimal places. Then press Check.

Try it yourself

$Use the figure to find x,h$

Use the figure to find x,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 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 RampTwo ObserversThe Landing Plane The Kite The Sun's Angle, Exactly