Two sides of a triangle have lengths and

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Two sides of a triangle

ABC

have lengths

AB = 6\,\text{cm}

and

AC = 8\,\text{cm}

. The included angle

\angle A = C

satisfies

\cos 2C = \dfrac{1}{2}

. (i) Express

\sin C

solely in terms of

\cos 2C

and hence determine the value of

\sin C

. (Take the principal value of

C

for a triangle.) (ii) Calculate the measure of angle

C

in degrees. (iii) Using the information above, find the area of triangle

ABC

correct to two decimal places.