Question

work out the total area of triangle ABC. calculate the area of AC. sides are:8.2cm and 13.5cm and angle 81 degrees

Answer 1

12.1

Explanation:

`(sin(81))/(13.5) =(sin(x))/(8.2)` = x=sin⁻¹
`((sin(81))/(13.5)* 8.2)`=36.9°

81°+36.9°=117.9°

180°-117.9°=62.1°

`(x)/(sin(62.1)) = (8.2)/(sin(36.9)) =(8.2)/(sin(36.9))*(62.1)=` 12.1cm

AC=12.1cm

Answer 2

54.67 cm²

Explanation:

Given that the two sides of Δ ABC are 8.2 cm and 13.5 cm and the angle included by those sides is 81°.

Let, b = 8.2 cm and c = 13.5 cm and ∠ A = 81°

Hence, area of triangle ABC, Δ =
`(1)/(2) bc \sin A`

⇒ Δ =
`(1)/(2) bc \sin 81`

⇒ Δ =
`(8.2 * 13.5 * \sin 81)/(2)`

⇒ Δ = 54.67 cm² (Answer)