Question

help. I can't do maths again​

Answer 1

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 )

Answer 2

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.