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Lynna [10]
3 years ago
5

A) Antoine's family is taking a summer vacation through the northern united states on day one of the trips the family will be tr

avelling 85 miles on day two of the trip they will travel 125 miles on the third day they will travel 176 miles how many kilometres will Antoine and his family travel each day? (calculate to the nearest kilometres.) b) How many miles and kilometres will they travel in total?
Mathematics
1 answer:
kirill115 [55]3 years ago
8 0

Answer:

<h2>621.207km</h2>

Step-by-step explanation:

We are expected to convert from miles to kilometer

first day 85 miles =136.794km

Second day 125 mile=201.168km

third day 176 miles =283.245km

Total distance covered is

136.794km+201.168km+283.245km=621.207km

Therefore the total distance in kilometer is 621.207km

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Given:

In ΔOPQ, m∠Q=90°, m∠O=26°, and QO = 4.9 feet.

To find:

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Solution:

In ΔOPQ,

m\angle O+m\angle P+m\angle Q=180^\circ        [Angle sum property]

26^\circ+m\angle P+90^\circ=180^\circ

m\angle P+116^\circ=180^\circ

m\angle P=180^\circ -116^\circ

m\angle P=64^\circ

According to Law of Sines, we get

\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}

Using the Law of Sines, we get

\dfrac{p}{\sin P}=\dfrac{o}{\sin O}

\dfrac{QO}{\sin P}=\dfrac{PQ}{\sin O}

Substituting the given values, we get

\dfrac{4.9}{\sin (64^\circ)}=\dfrac{PQ}{\sin (26^\circ)}

\dfrac{4.9}{0.89879}=\dfrac{PQ}{0.43837}

\dfrac{4.9}{0.89879}\times 0.43837=PQ

2.38989=PQ

Approximate the value to the nearest tenth of a foot.

PQ\approx 2.4

Therefore, the length of PQ is 2.4 ft.

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