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3 years ago

Can someone help me?

Mathematics

1 answer:

-BARSIC- [3]3 years ago

6 0

A tautology will have an infinite number of solutions, as it is true for all possible values of the variable by definition.

Example: 3(x+2) = 3x+6

All other linear equations in one variable will have one solution, which may include values that are undefined or indeterminate.

Examples:

... 3x-2 = 7 . . . solution is x=3

... x = 0/0 . . . . solution is an indeterminate number

... x = 1/0 . . . . solution is undefined

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4 years ago

Im giving 100 Points to anyone who could solve this for me please.

myrzilka [38]

Answer:

AB = 27.2

BC = 33.5

AC = 50.4

∠A = 38°

∠ABC = 112°

Step-by-step explanation:

<u>Trigonometric ratios</u>

$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$

where:

$\theta$ is the angle
O is the side opposite the angle
A is the side adjacent the angle
H is the hypotenuse (the side opposite the right angle)

$\implies \sf \cos(30^{\circ})=\dfrac{29}{BC}$

$\implies \sf BC=\dfrac{29}{\cos(30^{\circ})}$

$\implies \sf BC=\dfrac{58\sqrt{3}}{3}=33.5\:(nearest\:tenth)$

$\implies \sf \tan(30^{\circ})=\dfrac{BD}{29}$

$\implies \sf BD=29\tan(30^{\circ})$

$\implies \sf BD=\dfrac{29\sqrt{3}}{3}$

$\implies \sf \sin(38^{\circ})=\dfrac{BD}{AB}$

$\implies \sf AB=\dfrac{\dfrac{29\sqrt{3}}{3}}{\sin(38^{\circ})}$

$\implies \sf AB=27.2\:(nearest\:tenth)$

$\implies \sf \tan(38^{\circ})=\dfrac{BD}{AD}$

$\implies \sf AD=\dfrac{\dfrac{29\sqrt{3}}{3}}{\tan(38^{\circ})}$

$\implies \sf AD=21.4\:(nearest\:tenth)$

$\implies \sf AC=AD+DC=21.4+29=50.4$

The interior angles of a triangle sum to 180°

⇒ ∠A + 52° + 90° = 180°

⇒ ∠A = 180° - 90° - 52°

⇒ ∠A = 38°

⇒ ∠ABC + 38° + 30° = 180°

⇒ ∠ABC = 180° - 38° - 30°

⇒ ∠ABC = 112°

**I have checked the measures using a graphing programme - see attached**

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2 years ago