Find the missing side length

14

Step-by-step explanation:

Since they are similar triangles, we can use proportions

5              10

=

5+7       10+?

5              10

=

12          10+?

Using cross products

5( 10+?) = 12*10

Divide each side by 5

10+? = 12*10/5

10+? = 24

Subtract 10 from each side

10+?-10 = 24-10

? = 14

D

Step-by-step explanation:

Using the Cosine rule to find AC

AC² = BC² + AB² - (2 × BC × AB × cosB )

      = 18² + 12² - ( 2 × 18 × 12 × cos75° )

      = 324 + 144 - 432cos75°

      = 468 - 111.8

      = 356.2 ( take the square root of both sides )

AC = ≈ 18.9

-----------------------------------------

Using the Sine rule to find ∠ A

= ( cross- multiply )

18.9 sinA = 18 sin75° ( divide both sides by 18.9 )

sinA = , then

∠ A = ( ) ≈ 66.9°