Question

what is fi? 15w - 62 19w - 86 fi =

Explanation:

Step1: Identify congruent triangles

Since $\angle G=\angle I = 90^{\circ}$, $\angle GHF=\angle IHF = 40^{\circ}$ and $HF$ is common to both $\triangle GHF$ and $\triangle IHF$, by the Angle - Angle - Side (AAS) congruence criterion, $\triangle GHF\cong\triangle IHF$. So $GF = FI$.

Step2: Set up an equation

Set $15w - 62=19w - 86$.

Step3: Solve the equation for $w$

Subtract $15w$ from both sides: $-62 = 4w-86$. Then add 86 to both sides: $4w=24$, so $w = 6$.

Step4: Find the length of $FI$

Substitute $w = 6$ into the expression for $FI$ (either $15w - 62$ or $19w - 86$). Using $15w - 62$, we have $15\times6-62=90 - 62=28$.

Answer:

$28$