Given: △abc, m∠a=60°

m∠c=45°, ab=8

find: perimeter of △abc,

area of △abc

keep the answer in square root

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

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=

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)

its adding 5.5 each time

step-by-step explanation:

part a: 1.08

part b: 27.59