Question

Two buildings are 25 m apart. From the top of the shorter
building, the angles of elevation and depression of the top and bottom
of the taller building are 31° and 48° respectively. What is the height
of the taller building? Give your answer to the nearest metre.

Answer 1

Answer on Question #61877 – Math – Trigonometry

Question

Two buildings are $25\,\mathrm{m}$ apart. From the top of the shorter building, the angles of elevation and depression of the top and bottom of the taller building are $31{}^{\circ}$ and $48{}^{\circ}$ respectively. What is the height of the taller building? Give your answer to the nearest meter.

Solution

Using the bottom right triangle with a leg $c$ and an angle $48{}^{\circ}$

$$\tan 48{}^{\circ} = \frac{c}{25};$$ $$c = 25 \tan 48{}^{\circ}.$$

Using the top right triangle with a leg $b$ and an angle $31{}^{\circ}$

$$\tan 31{}^{\circ} = \frac{b}{25};$$ $$b = 25 \tan 31{}^{\circ}.$$

Adding two segments

$$a = b + c;$$ $$a = 25 \tan 48{}^{\circ} + 25 \tan 31{}^{\circ} = 25(1.11 + 0.6) = 42.75\,\mathrm{m} \approx 43\,\mathrm{m}.$$

Answer: $43\,\mathrm{m}$

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