Observation 82811

From the 40 m high observation deck, you can see the top of the poplar at a depth angle of 50*10' and the bottom of the poplar at a depth angle of 58*. Calculate the height of the poplar.

Correct answer:

h =  10.0358 m

Step-by-step explanation:

$$\begin{gathered} a=40\text{m} \\ \alpha =50°10^{\prime }=50°+\frac{10}{60}°=50.1667°\doteq 50.1667 \\ \beta =58°=58 \\ \tan \beta =a:x \\ x=a/\tan \beta =a/\tan 58°=40/\tan 58°=40/1.600335=24.99477\text{m} \\ \tan \alpha =b:x \\ b=x\cdot \tan \alpha =x\cdot \tan 50.166666666667°=24.9948\cdot \tan 50.166666666667°=24.9948\cdot 1.198818=29.9642\text{m} \\ h=a-b=40-29.9642=10.0358\text{m} \end{gathered}$$

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