Question

1

ed
H
I
6
mZI =
9
J
Write your answer as an integer or as a decimal rounded to the
nearest tenth.
01
HR
SE
OL

Answer 1

Answer: m∡Ɪ = 41.8 °

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Explanation:

Use the following mnemonic for right triangles:
SOH CAH TOA ;

in which:
sin = opposite/ hypotenuse ;

cos = adjacent/ hypotenuse ;

tan = opposite/adjacent ;

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We shall solve for the unknown " m∡Ɪ " ;
that is: "the measure of Angle Ɪ ".

From looking at the image attached:
Let's take at ∡Ɪ .

We see that the opposite side = 6 ; and that the hypotenuse = 9 ;
So, from the mnemonic mentioned ^above.

We use the SOH component:
sin Ɪ = opposite /adjacent ;

= 6/9 ;

which can be reduced:
" 6/9 = (6÷3)/(9÷3) = (2/3) ."

So: sin Ɪ = (2/3) ;

To solve for Ɪ ;

We use a calculator; to take the (arcsin) of Each Side of the equation:

[(arcsin) sin Ɪ ] = (arcsin) (
`(2)/(3)` ) ;

to get: Ɪ = 41.810314895779 ;
[Source used: Web2.0 Online Scientific Calculator].

Now, we shall round this calculated decimal number to the nearest tenth; that is; to the nearest single decimal point that appears after the non-decimal value.
We have: 41.81... ;

So: 41.8 ? Or: 41.9 ? If the digit in the hundredth place [that is, the next occurring decimal] is "4 or lesser" [i.e. "0, 1, 2, 3, or 4"] ; then we round down.

If the digit in the hundredth place [that is, the next occurring decimal] is "5 or greater" [i.e. "5, 6, 7, 8, or 9"] ; then we round down.

In our case, we have: "41.81..." ;
→ As such, we round down to "41.8" .

The correct answer is " m∡Ɪ = 41.8 °

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I hope this answer and explanation are helpful to you!

Best wishes!
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