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An isosceles triangle has a height of
12.5m and two equal angles that measure
55^(@). Determine the area of the triangle.

An isosceles triangle has a height of $12.5 \mathrm{~m}$ and two equal angles that measure $55^{\circ}$ . Determine the area of the triangle.

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Ratio and Quadratic equation

Full solution

Q. An isosceles triangle has a height of

12.5 \mathrm{~m}

and two equal angles that measure

55^{\circ}

. Determine the area of the triangle.

Calculate base length: Calculate the length of the base using trigonometry. $\newline$ Since the triangle is isosceles, the height bisects the base, creating two right triangles. Each has a base angle of $55$ degrees and a height of $12.5\,\text{m}$ . Using the tangent function: $\newline$ $\frac{\text{base}}{2} = \frac{\text{height}}{\tan(55°)}$ $\newline$ $\text{base} = 2 \times \left(\frac{12.5}{\tan(55°)}\right)$ $\newline$ $\text{base} \approx 2 \times \left(\frac{12.5}{1.4281}\right) \approx 17.47\,\text{m}$
Calculate triangle area: Calculate the area of the triangle. $\newline$ Area = $0.5 \times \text{base} \times \text{height}$ $\newline$ Area = $0.5 \times 17.47\,\text{m} \times 12.5\,\text{m}$ $\newline$ Area $\approx 0.5 \times 218.375 \approx 109.19$ square meters

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