Answer: x = 5, y = 12, z = 15
Step-by-step explanation:
Based on the given information, we know that these two triangles are similar. We can tell this because they both have a 90-degree angle and a 37-degree angle in corresponding places.
With this information, we can find the scale factor, or the constant of proportionality, between the two triangles.
9 / 3 = 3
These are right triangles, so we can use the Pythagorean theorem, where a and b are the legs and c is the hypotenuse. We will solve for x.
➜ The 3-4-5 is a well-known right triangle.
a² + b² = c²
3² + 4² = x²
25 = x²
x = 5
Lastly, we can find x and y using our constant of proportionality.
y = 4 * 3 = 12
y = 12
z = 3 * x = 3 * 5 = 15
z = 15
