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enot [183]
2 years ago
14

Help. I can't do maths again​

Mathematics
2 answers:
Goshia [24]2 years ago
5 0

Answer:

x ≈ 14.4 cm

Step-by-step explanation:

the third angle of the triangle = 180° - 40° - 46° = 94°

Using the Sine rule in the triangle

\frac{x}{sin46} = \frac{20}{sin94} ( cross- multiply )

x × sin94° = 20 × sin46° ( divide both sides by sin94° )

x = \frac{20sin46}{sin94} ≈ 14.4 cm ( to the nearest tenth )

harina [27]2 years ago
4 0

Answer:

14 cm (rounded to nearest whole number)

Step-by-step explanation:

Law of Sine:

\displaystyle \large{\dfrac{\sin A}{a} = \dfrac{\sin B}{b} = \dfrac{\sin C}{c} = 2R}

  • a,b,c are side lengths.
  • R is radius so 2R is diameter.
  • A,B,C are angles.

Given angles are:

  • 40°, 46°

Definition of Euclidean Triangle:

  • Sum of three interior angles equals 180°

Find another angle:

  • 40°+46°+B = 180°
  • 86+B = 180
  • B = 180-86
  • B = 94°

So another angle is 94°.

To find:

  • Value of x

Determine:

  • A = 46°
  • a = x cm
  • B = 94°
  • b = 20 cm

Therefore:

\displaystyle \large{\dfrac{\sin 46^{\circ}}{x} = \dfrac{\sin 94^{\circ}}{20}}

Multiply both sides by 20x:

\displaystyle \large{\dfrac{\sin 46^{\circ}}{x} \cdot 20x = \dfrac{\sin 94^{\circ}}{20} \cdot 20x}\\\displaystyle \large{20\sin 46^{\circ}= x\sin 94^{\circ}}

Divide both sides by \displaystyle \large{\sin 94^{\circ}}:

\displaystyle \large{\dfrac{20\sin 46^{\circ}}{\sin 94^{\circ}} = \dfrac{x\sin 94^{\circ}}{\sin 94^{\circ}}}\\\displaystyle \large{\dfrac{20\sin 46^{\circ}}{\sin 94^{\circ}} = x}

Evaluate the expression, hence:

\displaystyle \large{x = 14.42...}

Round to nearest whole number:

\displaystyle \large{x = 14}

Therefore, the value of x is 14 cm.

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