To find the distance from Lucas to Maria, we can use the fact that the angle formed at Lucas is 90°, making the triangle a right triangle. We can use the Pythagorean Theorem to calculate the distance.
Let x be the distance from Lucas to Maria. Therefore, the right triangle formed by Ava, Lucas, and Maria can be solved as follows:
(12)^2 + x^2 = (12 + x)^2
144 + x^2 = 144 + 24x + x^2
144 = 24x
x = 6 feet
Therefore, the distance from Lucas to Maria is 6 feet.
To find the distance from Ava to Maria, we can use the sine of the 40° angle at Ava's position. Let y be the distance from Ava to Maria.
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