Answer:
<u>Part 1) </u>
Part a)
Part b)
(three different ways in the procedure)
<u>Part 2)</u>
First triangle (triangle a)
Part a)
Part b) 
Part c) 
Second triangle (triangle b)
Part a)
Part b) 
Part c)
Step-by-step explanation:
Part 1)
<u>Part A</u>
we know that
In the right triangle ABC
we have



Substitute and solve for b

<u>Part B</u>
First way
we know that
In the right triangle ABC

we have



Substitute and solve for a

Second way
Applying the Pythagoras theorem

we have


substitute and solve for a



Third way
we know that
In the right triangle ABC

we have



substitute and solve for a

Part 2)
<u> triangle a</u>
we have

Step 1
<u>Find the measure of length side c</u>
Applying the law of cosines
substitute
Step 2
<u>Find the measure of angle A</u>
Applying the law of sines

we have


substitute and solve for A
Step 3
<u>Find the measure of angle B</u>
Remember that the sum of the internal angles of a triangle must be equal to
degrees
so

we have


substitute
<u> triangle b</u>
we have


Step 1
<u>Find the measure of angle A</u>
Remember that the sum of the internal angles of a triangle must be equal to
degrees
so

we have


substitute
Step 2
<u>Find the measure of side AC</u>
Applying the law of sines

we have




substitute and solve for b

Step 3
<u>Find the measure of side BC</u>
Applying the law of sines

we have




substitute and solve for a
