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 $\displaystyle \large{\sin 94^{\circ}}$ :

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