Answer: [tex]\bold{a=8,\quad b=2\sqrt{17}}[/tex]
Step-by-step explanation:
First, I like to draw the triangles so they look the same.
- right angle on the bottom right
- one tick mark angle on the top
- no tick mark angle on the bottom left
Now, because the angles from the top triangle are congruent to the triangle on the bottom, they are similar triangles. Therefore, their sides form a proportion. From drawing I created, the sides match up as follows:
- left (top) triangle → the right side = 32
- left (top) triangle → the base = a
- right (bottom) triangle → the right side = a
- right (bottom) triangle → the base = 2
Next, set up the proportions
[tex]\dfrac{32}{a} =\dfrac{a}{2}[/tex]
[tex]=\dfrac{64}{a^2}[/tex]
[tex]= 8[/tex]
Lastly, Use the Pythagorean to solve for b:
2² + 8² = b²
4 + 64 = b
68 = b²
2√17 = b
