Problem solving application engineering geometry need 1-4

Problem 1)

20 feet

We have two base angles that are congruent, so that implies we have an isosceles triangle. With isosceles triangles there are exactly two congruent sides. So PD = PC = 20



Problem 2)

168 feet

Each leg of each triangle is equal to 42 ft. The reason why is because we have congruent triangles so all of the corresponding parts are congruent. For any given right triangle, the two legs are equal in length. 

We have 4 sections of 42 ft, so 4*42 = 168 ft in total



Problem 3)

Yes it is long enough

Let a, b, and c be the three sides

a = 5
b = 4
c = 2

Note these three properties:
Property 1: a+b = 5+4 = 9 is larger than c = 2
Property 2: b+c = 4+2 = 6 is larger than a = 5
Property 3: a+c = 5+2 = 7 is larger than b = 4

Since all three properties hold true, this means that we can construct a triangle with these side lengths. Put another way, take any two sides and add them up. The result being larger than the third side allows a triangle to be formed. This is the triangle inequality theorem. 



Problem 4)

55 degrees

x = base angle

we have two base angles plus the vertex angle of 70 degrees

The three angles (x, x, 70) must add to 180

x+x+70 = 180
2x+70 = 180
2x+70-70 = 180-70
2x = 110
2x/2 = 110/2
x = 55

Therefore, each base angle is 55 degrees