Helll!
(05.04 mc)
in δxyz, x = 8.3 meters, y = 9 meters, and z = 15 meters. find the remaining measurements of the triangle, and round your answers to the nearest tenth.
a: ∠x = 56.9°, ∠y = 66.6°, ∠z = 56.5°
b: ∠x = 28.6°, ∠y = 31.2°, ∠z = 120.2°
c: ∠x = 56.9°, ∠y = 66.6°, ∠z = 120.2°
d: ∠x = 28.6°, ∠y = 31.2°, ∠z = 56.5°

  b:   ∠x = 28.6°, ∠y = 31.2°, ∠z = 120.2°

step-by-step explanation:

this is one of those questions where "test taking skill" is all you need. the only answer that has angles that sum to 180° is the one shown above. the remaining choices do not describe the angles of a triangle.

if you want to do more work than simply adding the offered numbers, you can also check them against the law of sines. it should be true that

  x/sin(x) = y/sin(y) = z/sin(z)

and all of these ratios must be greater than 15, the longest side length.

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if you want to solve the triangle from scratch, i'd suggest solving for the largest angle using the law of cosines.

  z² = x² +y² -2xy·cos(z)

  z = arccos((x² +y² -z²)/(2xy)) = arccos(-75.11/149.4) = 120.182°

now you can find y from the law of sines

  y = arcsin(y/z·sin(z)) = 31.242°

x = 17

step-by-step explanation:

in the given figure, two triangles are inscribed in a circle where ∠bae ≅ ∠dae which makes the side be and de equal so we can write it as:

3x - 24 = x + 10

solving this equation for x to get:

3x - x = 10 + 24

2x = 34

x = 34/2

x = 17

therefore, the value of x = 17.

3 is greater then both of those numbers