To find the distance from Lucas to Maria, we can use the trigonometric relationships in a right triangle. Since the angle at Lucas is 90°, we know that the triangle is a right triangle. Let's denote the distance from Lucas to Maria as x.
Using trigonometry, we can use the cosine function in this case:
cos(40°) = adjacent/hypotenuse
cos(40°) = 12/x
x = 12/cos(40°)
x ≈ 14.7 feet
Therefore, the distance from Lucas to Maria is approximately 14.7 feet.
To find the distance from Ava to Maria, we can use the trigonometric relationships as well. Let's denote this distance as y.
Using the sine function in this case:
sin(40°) = opposite/hypotenuse
sin(40°) = y/12
y = 12*sin(40°)
y ≈ 7.7 feet
Therefore, the distance from Ava to Maria is approximately 7.7 feet.
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.
What is the distance from Lucas to Maria in feet?
What is the distance from Ava to Maria in feet?
1 answer
1 answer