Question

22. Which is an expression for the area
of ABC?

Answer 1

C

Explanation:

the area (A) of the triangle is calculated as

A =
`(1)/(2)` product of 2 sides × sin ( angle between the 2 sides )

We are only given 1 side (AC) so require to find AB or BC using the Sine rule

the third angle B = 180° - (48 + 67)° = 180° - 115° = 65°

using the Sine rule to find AB

`(AB)/(sin67)` =
`(15)/(sin65)` ( cross- multiply )

AB × sin65° = 15 × sin67° ( divide both sides by sin65° )

AB =
`(15sin67)/(sin65)`

Now

A =
`(1)/(2)` × AB × AC sin48°

=
`(1)/(2)` ×
`(15sin67)/(sin65)` × 15sin48°

=
`(15sin67)/(2sin65)` × 15sin48° → C