Answer:
x = 30.91 cm , y = 29,86 cm and z = 39.30 cm.
Total area of wood = 2942.54 cm^2.
Explanation:
sin 15 =8/x
x = 8 / sin 15
x = 30.91 cm.
and
tan 15 = 8/y
y = 8 / tan 15
= 29.86 cm.
The value of z can be found using the Pythagoras theorem:
50^2 = x^2 + z^2
z^2 = 20^2 - x^2 = 50^2 - 30.91^2
z^2 = 1554.57
z = √1554.57
= 39.30 cm.
b. The area consists of 3 rectangles :- 1. sides x and z 2. sides z and 8 and the other has sides z and y. Also 2 triangles of height 8 and base length y cm.
Total area = 30.91 * 39.30 + 8 * 39.30 + 29.86 * 39.30 + 2 * 0.5 * 8 * 29.86
= 2942.54 cm^2.