## Solve Lesson 16 Page 79 Math 10 – Kite >

Topic

An’s family owns a triangular piece of land. The length of the fence MN is 150 m, the length of the fence MP is 230 m. Angle between two fences MN and MP is 1100 (Figure 21)

a) How many square meters is the area of ​​land that An’s family owns (round up to tenths)?

b) Fence length NP how many meters (round to tenths)?

Solution method – See details

Step 1: Use the area formula $$S = \frac{1}{2}MN.MP\sin M$$ to calculate the area ∆MNP

Step 2: Use the cosine theorem to calculate the length NP

Step 3: Conclusion

Detailed explanation

a) $${S_{MNP}} = \frac{1}{2}MN.MP\sin M = \frac{1}{2}.150.230.\sin {110^0} \approx 16209.7$$ ( m2)

So the area of ​​land that An’s family owns is 16209.7 m .2

b) Apply the law of cosines toABC we have: $$N{P^2} = M{N^2} + M{P^2} – 2.MN.MP.\cos M$$

$$\Rightarrow NP = \sqrt {M{N^2} + M{P^2} – 2.MN.MP.\cos M}$$$$= \sqrt {{{150}^2} + { {230}^2} – 2,150,230.\cos {{110}^0}} \approx 314.6$$(m)

So the length of the fence NP is 314.6 m