Question

Please help me with this problem

Answer 1

∠DEF = 60

x = 11.4

y = 4

Explanation:

Step 1: State what is known

The question tells us that Triangle ABC is similar to Triangle EFD, We know similar angles share the same angles and the sides are similar to the corresponding side

Step 2: Find the unknown angle

Because we know the triangles are similar we need to find ∠BAC to solve for 'z'

z = 180 - 55 - 65

z = 60

Step 3: Find the unknown side with the ratio

We know 1 pair of sides BC and DF and it gives us a ratio of BC : DF or 3 : 1

We can set the ratios equal to an unknown side to solve:

3 : 1 = 12 : y

We can multiple 3 : 1 by 4 to get the 'y'

12 : 4

y = 4

3 : 1 = x : 3.8

We can multiple 3 : 1 by 3.8 to get 'x'

11.4 : 3.8

x = 11.4

Therefore ∠DEF = 60, side x = 11.4 and side y = 4

Answer 2

y = 4

Explanation:

If two triangles are similar then,

i) Corresponding angles will be equal

ii) Corresponding sides will be in the same ratio.

`(AC)/(EF)=(CB)/(FD)\\\\\\(12)/(y)=(15)/(5)\\\\`

Cross multiply,

12*5 = y*15

y*15 = 12*5

`y=(12*5)/(15)\\`

y = 4