Question

Please help find the variable in both triangles.

Answer 1

Explanation:

these are projections from V and W to the same projection "screen" (SU and YX).

since the angles are equal, the ratio between projection beam length and screen length must be the same.

so,

6.

24/14 = 48/x

48/28 = 48/x

x = 28

7.

besides the projection principle, we have a basic triangle situation :

the bisector of the angle W is also bisecting the opposing side YX. that means that this is an isoceles triangle (both legs are equally long).

therefore,

y = 4×sqrt(2)

Answer 2

`\textsf{6.} \quad x = 28`

`\textsf{7.} \quad y = 4√(2)`

Explanation:

What is an angle bisector?

An angle bisector is a line that divides an angle into two equal parts.

Angle Bisector Theorem

An angle bisector in a triangle divides the opposite side into two segments which are in the same proportion as the other two sides of the triangle.

Question 6

Applying the Angle Bisector Theorem:

`\implies (UT)/(TS)=(VU)/(VS)`

`\implies (x)/(14)=(48)/(24)`

Cross multiply:

`\implies 24 \cdot x=48 \cdot 14`

`\implies 24x=672`

Divide both sides by 24:

`\implies (24x)/(24)=(672)/(24)`

`\implies x=28`

Question 7

Applying the Angle Bisector Theorem:

`\implies (XZ)/(ZY)=(WX)/(WY)`

`\implies (4)/(4)=(y)/(4√(2))`

Carry out the division on the left side:

`\implies 1=(y)/(4√(2))`

Multiply both sides by 4√2:

`\implies 1\cdot 4√(2)=(y)/(4√(2))\cdot 4√(2)`

`\implies 4√(2)=y`

`\implies y=4√(2)`