Question

On paper, sketch 2 sizes of similar right triangles, each having one of its non-right angles as a 22 degree angle. On the smaller triangle, label the hypotenuse with a length of 6 cm. On the larger triangle, label the hypotenuse with 12 cm and the side opposite the 22 degree angle with a length of 8 cm. Now, determine the length of the side opposite the 22 degree angle in the smaller triangle. (1 point) The side opposite the second triangle's 22 degree angle has a length of cm.

Answer 1

its 9

Answer 2

To determine the length of the side opposite the 22 degree angle in the smaller triangle, we can use the properties of similar triangles.

Given that the larger triangle has the hypotenuse labeled as 12 cm and the side opposite the 22 degree angle as 8 cm, we can set up a ratio between the triangles.

The ratio of the hypotenuses of the smaller triangle to the larger triangle is:
\[
\frac{6 \text{ cm}}{12 \text{ cm}} = \frac{1}{2}
\]

Since the triangles are similar, the lengths of corresponding sides are in the same ratio. Therefore, the length of the side opposite the 22 degree angle in the smaller triangle (let's call it \(x\)) can be found using the corresponding side in the larger triangle:

\[
\frac{x}{8 \text{ cm}} = \frac{1}{2}
\]

Now solving for \(x\):
\[
x = 8 \text{ cm} \times \frac{1}{2} = 4 \text{ cm}
\]

Thus, the length of the side opposite the 22 degree angle in the smaller triangle is **4 cm**.