Question

Ravi has a plane triangular pilot ABC in which AB = 9m, BC = 7m and CA = 8m. A Flag is hoisted at the midpoint M of the side AC. If the top of the Flag subtends an angle 15° at the corner B of the plot, determine the height of the Flag From the ground.

Answer 1

Answer on Question #57419 – Math – Geometry

Question

Ravi has a plane triangular plot ABC in which AB = 9m, BC = 7m and CA = 8m. A Flag is hoisted at the midpoint M of the side AC. If the top of the Flag subtends an angle $15{}^{\circ}$ at the corner B of the plot, determine the height of the Flag From the ground.

Solution

The general formula for the length of median is

$$BM = m_b = \frac{1}{2} \sqrt{2(a^2 + c^2) - b^2}$$

Given $M$ is the midpoint of the side AC. The length of median $BM$ is

$$BM = \frac{1}{2} \sqrt{2(7^2 + 9^2) - 8^2} = 7\,m.$$

Let $N$ be the top of the Flag, $\angle MBN = 15{}^\circ$ is given. From the right triangle $NMB$ the height of the Flag from the ground is

$$h = NM = BM \tan 15{}^\circ = 7 \cdot \tan 15{}^\circ = 1.8756\,m.$$

Answer: 1.8756 m.

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