Question

Solve the question in the picture. I know that there is an equation where you'll get root 25 - x^2 plus root 32 - x^2 equals 7, but there has to be a better way.

Answer 1

CM = 4

Explanation:

set CM=x and BM=y AM= 7-y

right triangle BMC: x² = 5² - y² = 25 - y² ... (1)

right triangle AMC: x² = (4√2)² - (7-y)² = 32 - 49 +14y - y² = -17 + 14y -y² ...(2)

(1)-(2): 0 = 42 - 14y

14y = 42

y (BM) = 3

x² (CM²) = 25 - 3² = 16

x (CM) = 4 (height is positive)