Question

Find z of the diagonal triangle. Also, complete b.

Answer 1

Answer:

x = 30.91 cm , y = 29,86 cm and z = 39.30 cm.

Total area of wood = 2942.54 cm^2.

Step-by-step 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.