QuestionQuestion 9
Find the measure of the indicated angle to the nearest degree. (ROUND TO NEAREST NUMBER, you do not need to write the degree symbol, just the number)
Studdy Solution
STEP 1
What is this asking?
We need to find the angle in a right triangle, knowing the opposite side and the hypotenuse.
Watch out!
Make sure your calculator is in degree mode, not radians!
Also, remember SOH CAH TOA.
STEP 2
1. Set up the trigonometric ratio.
2. Solve for the angle.
STEP 3
We're dealing with the **opposite** side and the **hypotenuse**.
Which trigonometric function uses those?
It's **sine**!
Remember SOH CAH TOA?
SOH means .
STEP 4
Let's call our mystery angle .
We know the **opposite** side is and the **hypotenuse** is .
So, we can write our equation:
STEP 5
To get by itself, we need to use the **inverse sine** function, also written as or .
Applying this to both sides gives us:
STEP 6
Now, grab your calculator!
Make *absolutely sure* it's in **degree mode**.
Calculate that inverse sine:
STEP 7
The problem asks us to round to the nearest degree.
So, our **final answer** is .
STEP 8
The angle is .
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