Question

Study the diagram below and calculate the area of triangle MPN. (Round off to two decimal places.)

Non-right-angled triangle MPN, where PM=15 meters, PN=15 meters, NM=17 meters and MPN=69 degrees.

Answer 1

To calculate the area of triangle MPN, we can use the formula for the area of a triangle given two sides and the included angle:

\[
\text{Area} = \frac{1}{2} \times a \times b \times \sin(C)
\]

Where:
- \( a \) and \( b \) are the lengths of the two sides,
- \( C \) is the included angle.

In this case:
- \( a = PM = 15 \) meters,
- \( b = PN = 15 \) meters,
- \( C = \angle MPN = 69^\circ \).

Now substituting the values into the formula:

\[
\text{Area} = \frac{1}{2} \times 15 \times 15 \times \sin(69^\circ)
\]

To perform the calculation, we first need to find \(\sin(69^\circ)\). Using a calculator:

\[
\sin(69^\circ) \approx 0.93358
\]

Now substitute this value back into the area formula:

\[
\text{Area} = \frac{1}{2} \times 15 \times 15 \times 0.93358
\]
\[
\text{Area} = \frac{1}{2} \times 225 \times 0.93358
\]
\[
\text{Area} = 112.5 \times 0.93358 \approx 105.15
\]

So, rounding to two decimal places, the area of triangle MPN is:

\[
\boxed{105.15} \text{ square meters}
\]