This is the concept of trigonometry, to get the possible length of side a we use the sine rule which states that:
a/sin A=b/sin B=c/sin B
where;
a,b and c are the sides
A,B and C are the angles
thus the value of A could be as follows;
assuming the triangle is an isosceles triangle, the base angles will be:
(180-40)/2=70
thus;
15/sin 70=a/sin 40
a=(15sin40)/sin70
a=10.26 inches
thus the possible size of a=10.26 inches
Answer:
7.840136054421769
Step-by-step explanation:
Short Answer: y = 36°
Remark
What an interesting question!! The first thing you have to do is find out what the interior angle of a regular pentagon is. After you have done that, you can calculate y.
Method.
The exterior angles of a regular figure add up to 360°.
Step One
Find out the size of the exterior angles of a regular pentagon.
There are 5 such angles. They add up to 360°
5x = 360 Divide by 5
x = 360 / 5
x = 72°
Step Two
Find out the value of the interior angles of a pentagon.
Method
The interior and exterior angles add up to 180°
Exterior Angle + Interior Angle = 180°
Exterior angle = 72 degrees
72° + Interior Angle = 180° Subtract 72 from both sides.
Interior Angle = 180° - 72°
Interior Angle = 108°
Step Three
Solve for y.
There are 3 tiles each with an angle of 108° that are placed together. So y + 3 interior angles = 360°
y + 3*interior angles = 360°
y + 3*108 = 360
y + 324 = 360 Subtract 324 from both sides.
y = 360 - 324
y = 36°
I think it’s 20 I had this on my test