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3 years ago

X, Y and Z form the vertices of a triangle. XY = 12.4m, XZ = 10.4m and YZ = 8.7m. Find the angle ∠ YXZ rounded to 1 DP.

Mathematics

1 answer:

sweet-ann [11.9K]3 years ago

6 0

Answer:

43.8°

Step-by-step explanation:

Applying,

Cosine rule,

From the diagram attached,

x² = y²+z²-2yxcos∅.................... Equation 1

where ∅ = ∠YXZ

Given: x = 8.7 m, y = 10.4 m, z = 12.4 m

Substitute these values into equation 1

8.7² = 10.4²+12.4²-[2×10.4×12.4cos∅]

75.69 = (108.16+153.76)-(257.92cos∅)

75.69 = 261.92-257.92cos∅

collect like terms

257.92cos∅ = 261.92-75.69

257.92cos∅ = 186.23

Divide both sides by the coefficient of cos∅

cos∅ = 186.23/257.92

cos∅ = 0.722

Find the cos⁻¹ of both side.

∅ = cos⁻¹(0.7220)

∅ = 43.78°

∅ = 43.8°

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Answer:

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Step-by-step explanation:

Sofia and Diego drive to work.

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We convert miles to km

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72 miles = x

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Speed = Distance/Time

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2 years ago

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Answer:

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Andre45 [30]

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Replace f(x) by y:
y=2x+4/3

Solving for x:
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(3y-4)/3=2x

Dividing both sides of the equation by 2:
[(3y-4)/3]/2=2x/2
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Then, for x=6
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