Question

14 Type the correct answer in each box. Use numerals instead of words. a 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.​

Answer 1

Explanation:

Answer:

Maria–Ava: 15.7 feet

Lucas–Maria: 10.1 feet

angle at Maria: 50°

Explanation:

The cosine and tangent functions are useful here. The relevant relations are ...

Cos = Adjacent/Hypotenuse

Tan = Opposite/Adjacent

__

The distance from Maria to Ava (ma) is the hypotenuse of the triangle, so we have ...

cos(40°) = 12/ma

ma = 12/cos(40°) ≈ 12/0.76604 ≈ 15.7 . . . feet

__

The distance from Lucas to Maria (ml) is the side opposite the given angle, so we have ...

tan(40°) = ml/12

ml = 12·tan(40°) ≈ 12·0.83910 ≈ 10.1 . . . feet

__

The angle formed at Maria's position is the complement of the other acute angle in the right triangle:

M = 90° -40° = 50°

In summary, ...

Maria–Ava: 15.7 feet

Lucas–Maria: 10.1 feet

angle at Maria: 50°

Answer 2

• Maria–Ava: 15.7 feet
• Lucas–Maria: 10.1 feet
• angle at Maria: 50°

Explanation:

The cosine and tangent functions are useful here. The relevant relations are ...

Cos = Adjacent/Hypotenuse

Tan = Opposite/Adjacent

__

The distance from Maria to Ava (ma) is the hypotenuse of the triangle, so we have ...

cos(40°) = 12/ma

ma = 12/cos(40°) ≈ 12/0.76604 ≈ 15.7 . . . feet

__

The distance from Lucas to Maria (ml) is the side opposite the given angle, so we have ...

tan(40°) = ml/12

ml = 12·tan(40°) ≈ 12·0.83910 ≈ 10.1 . . . feet

__

The angle formed at Maria's position is the complement of the other acute angle in the right triangle:

M = 90° -40° = 50°

In summary, ...

• Maria–Ava: 15.7 feet
• Lucas–Maria: 10.1 feet
• angle at Maria: 50°