Indirect Measurement Math Example 2

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Example 2

hard
From a point 6060 m from the base of a building, the angle of elevation to the top is 50°50°. Find the height of the building to the nearest metre.

Solution

  1. 1
    Draw a right triangle: horizontal distance =60= 60 m (adjacent side), building height hh (opposite side), angle of elevation =50°= 50°.
  2. 2
    Apply tan⁡θ=oppositeadjacent\tan\theta = \dfrac{\text{opposite}}{\text{adjacent}}: tan⁡50°=h60\tan 50° = \dfrac{h}{60}.
  3. 3
    Solve: h=60×tan⁡50°≈60×1.1918≈71.5h = 60 \times \tan 50° \approx 60 \times 1.1918 \approx 71.5 m.
  4. 4
    Round to nearest metre: h≈72h \approx 72 m.

Answer

The building is approximately 7272 m tall.
The tangent ratio connects an angle of elevation to the ratio of vertical height over horizontal distance. This allows measurement of inaccessible heights using only a ground distance and an angle measurement.

About Indirect Measurement

Indirect measurement finds unknown lengths by using proportional relationships instead of direct measuring tools.

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