Question

these triangles are similar. solve for x. 14, 21, 64°, 76° (on the first triangle); 8, x, 76°, 64° (on the second triangle). x = ?

Explanation:

Step1: Match corresponding sides

First, identify the corresponding sides of the similar triangles. The side of length 14 in the first triangle corresponds to the side of length 8 in the second triangle, and the side of length 21 in the first triangle corresponds to side $x$ in the second triangle.

Step2: Set up proportion

Since the triangles are similar, the ratios of corresponding sides are equal:
$\frac{14}{8} = \frac{21}{x}$

Step3: Cross-multiply to solve for x

Cross-multiply to isolate $x$:
$14x = 21 \times 8$
$14x = 168$

Step4: Divide to find x

Divide both sides by 14:
$x = \frac{168}{14}$

Answer:

12