Question

if $qr = 8$, $rs = 12$, and $uv = 14$, find the length of $overline{tu}$. round your answer to the nearest tenth if necessary. figures are not necessarily drawn to scale.

(there are two triangles: one with vertices q, r, s and angles 63°, 80°, 37°; the other with vertices v, t, u and angles 37°, 63°, 80°)

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

Explanation:

Step1: Confirm triangle similarity

Both triangles have identical angle measures (37°, 63°, 80°), so they are similar by AA similarity. Corresponding sides are proportional: $\frac{QR}{TU} = \frac{RS}{UV}$

Step2: Substitute given values

Plug in $QR=8$, $RS=12$, $UV=14$:
$\frac{8}{TU} = \frac{12}{14}$

Step3: Solve for $TU$

Cross-multiply and isolate $TU$:
$12 \cdot TU = 8 \cdot 14$
$TU = \frac{8 \cdot 14}{12} = \frac{112}{12} \approx 9.3$

Answer:

$9.3$