Math  /  Geometry

QuestionFind the measure of angle aa in degrees. Round to two decimal places as necessary.

Studdy Solution

STEP 1

What is this asking? We need to find the angle of a right triangle, knowing the **hypotenuse** and the **adjacent** side. Watch out! Make sure your calculator is in **degree** mode, not radians!
Also, remember SOH CAH TOA!

STEP 2

1. Set up the cosine ratio.
2. Solve for the angle.

STEP 3

Alright, let's dive in!
We've got a **right triangle**, a known **hypotenuse** of 1818, and an **adjacent** side of 1616.
Which trigonometric friend should we call upon?
It's **cosine** time!
Remember SOH CAH TOA?
Cosine is adjacent over hypotenuse.

STEP 4

So, we can set up our equation like this: cos(a)=adjacenthypotenuse\cos(a) = \frac{\text{adjacent}}{\text{hypotenuse}} cos(a)=1618\cos(a) = \frac{16}{18}We're on our way!

STEP 5

To find the angle aa, we need to unleash the **inverse cosine** (also known as arccos).
It's like hitting the "undo" button for cosine.

STEP 6

So, we get: a=arccos(1618)a = \arccos\left(\frac{16}{18}\right) a=arccos(89)a = \arccos\left(\frac{8}{9}\right)Remember, simplifying fractions makes life easier!

STEP 7

Now, grab your calculator, make sure it's in **degree** mode, and punch it in! a27.2660442a \approx 27.2660442^\circ

STEP 8

The problem asks us to round to two decimal places.
Looking at the third decimal place, which is a 6, we round up. a27.27a \approx 27.27^\circ Boom! We found our angle!

STEP 9

The measure of angle aa is approximately 27.2727.27^\circ.

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