Everything Maths Grade 11

CHAPTER 17. TRIGONOMETRY 17.5

Example 16: The Area Rule

QUESTION

Find the area of�ABC:

A

7

B C

50 ◦

SOLUTION

�ABC is isosceles, therefore AB = AC = 7 andCˆ =Bˆ = 50◦. HenceAˆ = 180◦− 50 ◦−

50 ◦= 80◦. Now we can use the area rule to find the area:

A =

1

2

cbsinAˆ

=

1

2

. 7. 7. sin80◦
= 24, 13

Exercise 17 - 13

Draw sketches of the figures you use in this exercise.

1. Find the area of�P QR in which:

(a)Pˆ = 40◦; q = 9 and r = 25

(b)Qˆ = 30◦; r = 10 and p = 7

(c)Rˆ = 110◦; p = 8 and q = 9

2. Find the area of:

(a)�XY Z with XY = 6 cm; XZ = 7 cm andZˆ = 28◦

(b)�P QR with P R = 52 cm; P Q = 29 cm andPˆ = 58, 9 ◦

(c)�EF G with F G = 2, 5 cm; EG = 7, 9 cm andGˆ = 125◦

3. Determine the area of a parallelogram in which two adjacent sides are 10 cm and 13 cm and the
   angle between them is 55 ◦.


4. If the area of�ABC is 5000m^2 with a = 150m and b = 70m, what are the two possible sizes
   ofCˆ?