Question

if $ge = 21$, $ef = 22$, and $hi = 24$, find the length of $overline{jh}$. round your answer to the nearest tenth if necessary. figures are not necessarily drawn to scale.

two triangles are shown: triangle gef with angles at g (76°), f (63°), e (41°); triangle ijh with angles at i (63°), j (76°), h (41°).

answer attempt 1 out of 2
$jh = \square$ submit answer

Explanation:

Step1: Confirm triangle similarity

Triangles $GEF$ and $IJH$ have all corresponding angles equal ($76^\circ, 63^\circ, 41^\circ$), so they are similar.

Step2: Match corresponding sides

In $\triangle GEF$, side $GE=21$ corresponds to $\triangle IJH$ side $HI=24$; side $EF=22$ corresponds to side $JH$.

Step3: Set up proportion for similarity

$$\frac{JH}{EF} = \frac{HI}{GE}$$
Substitute values: $\frac{JH}{22} = \frac{24}{21}$

Step4: Solve for $JH$

$$JH = 22 \times \frac{24}{21}$$
Calculate: $JH = 22 \times \frac{8}{7} = \frac{176}{7} \approx 25.1$

Answer:

$25.1$