Find the value of x. Round to the nearest tenth.

Haha, I've done this recently! We are trying to find the hypotenuse, and we know the adjacent side. [tex]cosine = \frac{adjacent}{hypotenuse}[/tex], so we can use cosine to help us figure that out. cosine 37° = [tex]\frac{17.3}{x}[/tex]

On our calculator, we can determine that cosine of 37 degrees is 0.79863551004, and therefore 0.79863551004 = 17.3/x. Multiplying both sides by x gives 0.79863551004x = 17.3. Finally, all we have to do is divide 17.3 by 0.79863551004 and we get 21.661, rounded to the nearest tenth, 21.7!

I hope this helps!

VirαtKσhli VirαtKσhli · Answer 2 · 2022-02-17T16:25:36+01:00

Given :-

A right angled triangle is given to us .

To Find :-

The value of x.

Solution :-

In the given triangle one of the angle is 37° and one of its side is 17.3 . As we know that in a right angled triangle ,

[tex]\longrightarrow cos\theta =\dfrac{base}{hypotenuse}[/tex]

Substitute ,

[tex]\longrightarrow cos37^o =\dfrac{17.3}{x}[/tex]

Value of cos37° is 4/5 .

[tex]\longrightarrow \dfrac{4}{5}=\dfrac{17.3}{x} [/tex]

Cross multiply ,

[tex]\longrightarrow x =\dfrac{17.3\times 5}{4}[/tex]

Simplify ,

[tex]\longrightarrow \underline{\underline{x = 21.625}} [/tex]

Hence the value of x is 21.625.