NCHMCT JEE 2021 Question Paper with solutions for online practice

Question : 83 of 200

Marks: +1, -0

The length of side

A B

and side

B C

of a scalene traingle

A B C

are

12 {cm}

and

8 {cm}

respectively. The measure of angle

C

59^{∘}

. Find the length of side

A C

Solution:

Given,

∠ C=59^{∘} ≈ 60^{∘}

a=12 {cm}, b=8 {cm}

Now, by cosine formula,

\cos C \;\; =\;{a^{2}+b^{2}-c^{2}}/{2 a b}

⇒ \;\; \cos 60^{∘} \;\; =\;{(12)^{2}+(8)^{2}-(c)}/{2 × 12 × 8}

⇒ \;\; \;{1}/{2} \;\; =\;{144+64-(c)^{2}}/{192}

⇒ \;\; \;{1}/{2} \;\; =\;{208-c^{2}}/{192}

⇒ 416-2 c^{2} \;\; =192

⇒ 2 c^{2}=416-192

⇒ 2 c^{2}=224

⇒ c^{2}=112

⇒ c=√{112}=10.58

⇒ c=10.58 ≈ 10

⇒ c=10 {cm}

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