Answer:
x = 4.2
Step-by-step explanation:
We know that the two triangles shown are similar, as one of the angles that isn't the right angle of both triangles are congruent. We can tell from the hypotenuses that the ratio between the two triangles is 7:5. 4(7/5)=5.6.
Following the theorem, 5.6^2+x^2=7^2. 31.36 + x^2 = 49, x^2 = 17.64, x = 4.2.
A more direct way I would prefer when looking at this problem that doesn't involve the Pythagorean's theorem is that we can immediately recognize that the smaller triangle is a 3, 4, 5 triangle, so the height is 3. 3(7/5) is 4.2, letting us know the answer quickly.
