Question

What is the area of this triangle?

Enter your
answer as a decimal in the box. Round only your final
answer to the nearest tenth. 8, 28, 7

Answer 1

Use sine rule

Area:-

`\\ \sf\longmapsto (1)/(2)Base* Height sin\theta`

`\\ \sf\longmapsto (1)/(2)(8)(7)sin28`

`\\ \sf\longmapsto 28sin28`

`\\ \sf\longmapsto 13.1cm^2(Approx)`

Answer 2

13.1 cm² (nearest tenth)

Explanation:

Use the sine rule for area of a triangle with 2 sides and an included angle (SAS).

Sine rule for area

`\textsf{Area ABC}=\frac12ab \sin C`

(where
`a` and
`b` are the side lengths and
`C` is the included angle)

Given:

• 
  `a` = 8 cm
• 
  `b` = 7 cm
• 
  `C` = 28°

`\implies \textsf{Area}=\frac12\cdot 8 \cdot 7 \cdot\sin (28\textdegree)`

`=13.14520376...`

`= 13.1 \textsf{ cm}^2 \textsf{ (nearest tenth)}`