Area of a Triangle (Using Sine)
See how to find the area of a triangle using sine.
2 examples and their solutions.
Area of a Triangle (Using Sine)
Formula
A = 12ab sin θ
Example
A = 12⋅5⋅6⋅ sin 45°
= 5⋅3⋅1√2 - [1]
= 15√2⋅√2√2 - [2]
= 15√22
[1]
Close
Example
A = 12⋅4⋅7⋅sin 120°
= 2⋅7⋅(+sin (180° - 120°)) - [2]
= 2⋅7⋅sin 60°
= 2⋅7⋅√32 - [3]
= 7√3
[1]
120°: Quadrant II
In quadrant II, only sin is (+).
→ sin: (+)
In quadrant II, only sin is (+).
→ sin: (+)
[2]
120°: Quadrant II
→ Reference angle: 120° → (180° - 120°)
→ Reference angle: 120° → (180° - 120°)
[3]
sin 60°
SOH: Sine, Opposite side (√3), Hypotenuse (2)
SOH: Sine, Opposite side (√3), Hypotenuse (2)
Close