Answer:
perimeter = 28.68 cm
area = 15.48 cm^2
Step-by-step explanation:
1. complete the angles in the triangle. sum of all the angles in a triangle is 180 degrees.
therefore 180 - (60 +45) = 75
angle at B is 75 degrees
2. find the sides of the triangle using the sine formula for triangle
sin A/a = sin B/b = sin C/c
we have the angle at C and the side opposite C is also give, we can use that with any other
3. sin A/a = sin C/c
sin 60/a = sin 45/8
make a subject
a = 9.78 cm
4. sin A/a = sin B/b
sin 60/9.78 = sin 75/b
make b subject
b = 10.90 cm
with the three sides, we know that perimeter is the length around an object
adding all the lengths together will give the perimeter
perimeter = 10.90 + 8 + 9.78
= 28.68 cm
5. to find the area we need to find the high of the triangle since the expression for the area of a triangle is [tex]area =\frac{1}{2} bh[/tex]
6. bisecting the side BC will give have as 4.89 cm
7. using Pythagoras theorem we can find the height of the traingle
c^2 = a^2 + b^2
8^2=(4.89)^2 + b^2
64 - 23.9121 = b^2
b= [tex]\sqrt{40.0879}[/tex]
b =6.33 cm
insert this into the formula above will give the value for area
which is 15.48 cm^2
area = 1/2 (4.89)(6.33)
