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The diagram shows a right angled triangle. 11cm 8cm and x degrees. Find the size of angle x. Give your answer correct to 1 decimal place.​

The Diagram Shows A Right Angled Triangle 11cm 8cm And X Degrees Find The Size Of Angle X Give Your Answer Correct To 1 Decimal Place class=

Answer :

Given:

  • hyp= 11 cm
  • adj= 8 cm

Note that:

  • hyp: Hypotenuse
  • adj: Adjacent

To find:

The size of the unknown angle "x"

Solution:

We'll have to check which one is appropriate from SOHCAHTOA.

In this question hypotenuse and adjacent is given so, we'll have to use cos.

[tex]\large\boxed{Formula: cos \: (A)= \frac{adj}{hyp}}[/tex]

Let's solve!

Let's substitute the values according to the formula.

[tex]cos \: x= \frac{8}{11}[/tex]

We'll have to use cos inverse.

[tex]x= {cos}^{-1}( \frac{8}{11} )[/tex]

[tex]x= 43.34175823[/tex]

Now we'll have to round off to 1 decimal place.

The value in hundredths place is less than 5 so we won't have to round up.

So, the final answer is:

[tex]\large\boxed{x= 43.3°}[/tex]

Therefore, the size of the unknown angle "x" is 43.3°

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