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mixas84 [53]
3 years ago
13

In △ABC, m∠A=15 °, a=10 , and b=11 . Find c to the nearest tenth.

Mathematics
1 answer:
pshichka [43]3 years ago
4 0

Answer:

The answer is:

\bold{c\approx 20.2\ units}

Step-by-step explanation:

Given:

In △ABC:

m∠A=15°

a=10 and

b=11

To find:

c = ?

Solution:

We can use cosine rule here to find the value of third side c.

Formula for cosine rule:

cos A = \dfrac{b^{2}+c^{2}-a^{2}}{2bc}

Where  

a is the side opposite to \angle A

b is the side opposite to \angle B

c is the side opposite to \angle C

Putting all the values.

cos 15^\circ = \dfrac{11^{2}+c^{2}-10^{2}}{2\times 11 \times c}\\\Rightarrow 0.96 = \dfrac{121+c^{2}-100}{22c}\\\Rightarrow 0.96 \times 22c= 121+c^{2}-100\\\Rightarrow 21.25 c= 21+c^{2}\\\Rightarrow c^{2}-21.25c+21=0\\\\\text{solving the quadratic equation:}\\\\c = \dfrac{21.25+\sqrt{21.25^2-4 \times 1 \times 21}}{2}\\c = \dfrac{21.25+\sqrt{367.56}}{2}\\c = \dfrac{21.25+19.17}{2}\\c \approx 20.2\ units

The answer is:

\bold{c\approx 20.2\ units}

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