Ava, Lucas, and Maria are playing a game where they pass a pull-back toy to one another in a path that forms a right triangle. Ava sends the toy to Lucas. Then, Lucas sends the toy to Maria. Finally, Maria sends it back to Ava. The angle formed at Lucas' position measures 90° and the angle formed at Ava's position measures 40°. The distance from Ava to Lucas is 12 feet.

Ava is trying to determine the other measures of the triangle created by the toy's path. Give each distance in feet rounded to the nearest tenths place.

The distance from Maria to Ava is _ feet.

The distance from Lucas to Maria is _ feet.

The angle formed at Maria's position measures ___ degrees.

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joaobezerra joaobezerra · Answer 1 · 2022-02-10T12:04:51+01:00

Using relations in a right triangle, it is found that

The relations in a right triangle are given as follows:

The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.

The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.

The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.

In this problem, the situation is modeled by the graph given.

First, we have to remember that the sum of the internal angles of a triangle is of 180º, hence:

The angle formed at Maria's position measures 50 degrees.

Then, for the distance from Maria to Ava, which is the hypotenuse:

[tex]\sin{50^\circ} = \frac{12}{h}[/tex]

[tex]h = \frac{12}{\sin{50^\circ}}[/tex]

[tex]h = 15.66[/tex]

Hence:

The distance from Maria to Ava is 15.66 feet.

Finally, for the distance from Lucas to Maria:

[tex]\sin{40^{\circ}} = \frac{d}{15.66}[/tex]

[tex]d = 15.66\sin{40^{\circ}} = 10.07[/tex]

The distance from Lucas to Maria is 10.07 feet.

To learn more about relations in a right triangle, you can take a look at https://brainly.com/question/10467648