Question

Find the value of x. Round to the nearest degree. show your work.

Answer 1

Answer:

$\large\boxed{x=51}$

Step-by-step explanation:

Use sine:

$sine=\dfrac{opposite}{hypotenuse}$

We have:

$opposite=7\\\\hypotenuse=9$

Substitute:

$\sin x^o=\dfrac{7}{9}\\\\\sin x^o=0.777...\\\\\sin x\approx0.7778\to x\approx51^o$

Answer 2

To solve such questions we need to know about trigonometric ratios.

Trigonometric functions

$\bold{Sin(\theta)=\dfrac{Perpendicular}{Hypotenuse}}$

$\bold{cos(\theta)=\dfrac{Base}{Hypotenuse}}$

$\bold{tan(\theta)=\dfrac{Perpendicular}{Base}}$

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

The value of x is 51.075°.

Explanation

Given to us,

• AB = 7 units,
• AC = 9 units,

We know for a right-angled triangle, sinθ  is given as,

$\bold{Sin(\theta)=\dfrac{Perpendicular}{Hypotenuse}}$

where,

θ is the angle,

Perpendicular is the side opposite to the angle,

the hypotenuse is the longest side of the triangle and it is always opposite to the right angle.

In ΔABC, for ∠x,

• Perpendicular = AB = 7 units,
• hypotenuse = AC = 9 units,

substituting the values into the formula for Sin(x),

$\bold{Sin(x)= \dfrac{AB}{AC}= \dfrac{7}{9}}$,

$sin(x) = 0.7778\\x = sin^{-1} 0.7778\\x = 51.057$

Hence, the value of x is 51.075°.

Learn more about trigonometric ratios:

https://brainly.com/question/3770177