Problems with trigonometry and the area of a triangle
Answers are for parents and teachers.
1
Two sides of a triangle are 12 and 9 with a 30° angle between them. Find the area.
27
2
A parallelogram has sides 7 and 4 and an angle of 30°. Find its area.
14
3
A quadrilateral has diagonals 6 and 20 meeting at 90°. Find its area.
60
4
A right triangle has hypotenuse 16 and an acute angle of 60°. Find the leg opposite the 60° angle.
8√3
5
Why does the quadrilateral area formula use the sine of the angle between the diagonals?
The diagonals split the quadrilateral into four triangles whose areas add up to ½·d₁·d₂·sinφ.