Question

1. firefighters dig a triangular trench around a forest fire to prevent the fire from spreading. two of the trenches are 800 m long and 650 m long. the angle between them is 30°. determine the area that is enclosed by these trenches.
2. a mayan pyramid at chichén-itzá has stairs that rise about 64 cm for every 71 cm of run. at what angle do these stairs rise?

Explanation:

Step1: Recall the formula for the area of a triangle

The formula for the area of a triangle when two sides \(a\) and \(b\) and the included angle \(\theta\) are known is \(A=\frac{1}{2}ab\sin\theta\).

Step2: Identify the values of \(a\), \(b\), and \(\theta\)

Here, \(a = 800\space m\), \(b=650\space m\), and \(\theta = 30^{\circ}\).

Step3: Substitute the values into the formula

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Answer:

The area is \(130000\space m^{2}\)