In ΔXYZ, x = 19.2 meters, y = 21 meters, and z = 19.1 meters. Find the remaining measurements of the triangle, and round your answers to the nearest tenth.
∠X = 57°, ∠Y = 66.5°, ∠Z = 56.5°
∠X = 28.6°, ∠Y = 91.2°, ∠Z = 56.5°
∠X = 28.6°, ∠Y = 91.2°, ∠Z = 60.2°
∠X = 57°, ∠Y = 66.5°, ∠Z = 60.2°

∠X = 57°, ∠Y = 66.5°, ∠Z = 56.5°

Step-by-step explanation:

step 1

Find the measure of angle X

Applying the law of cosines

substitute the given values

step 2

Find the measure of angle Y

Applying the law of cosines

substitute the given values

step 3

Find the measure of angle Z

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

so

substitute the given values

solve for Z

36 girls

step-by-step explanation:

the 48 boys is 4 parts of the ratio

divide 48 by 4 to obtain one part of the ratio

= 12 ← 1 part of the ratio

3 parts = 3 × 12 = 36 ← number of girls