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Express the trig ratios as fractions in simplest terms.
S
T
U
18
30
24
Answer
Attempt 1 out of 2

sin TT =

cos UU =

sin TT and cos UU
.
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DO IT BASE OFF OF THIS Example Problems
Express the trig ratios as fractions in simplest terms.
H
I
J
20
52
48
opposite ∠I
adjacent to ∠J
hypotenuse
SOH CAH TOA
SOH CAH TOA
cos , J, equals, start fraction, adjacent, divided by, hypotenuse, end fraction, equals, start fraction, 48, divided by, 52, end fraction, equals, start fraction, 12, divided by, 13, end fraction
cos J=
hypotenuse
adjacent
​
=
52
48
​
=
13
12
​

Simplify the fraction
sin , I, equals, start fraction, opposite, divided by, hypotenuse, end fraction, equals, start fraction, 48, divided by, 52, end fraction, equals, start fraction, 12, divided by, 13, end fraction
sin I=
hypotenuse
opposite
​
=
52
48
​
=
13
12
​

cos JJ and sin II are equal because start overline, H, J, end overline
HJ
is adjacent to angle, J∠J and opposite angle, I∠I.
Previous Example
SIN = T
COS= U

Answer 1

To solve the given problem, we first need to identify the angle measurements and the sides of the right triangle. Based on the labeling provided (S, T, U) and the side lengths given (18, 30, 24), we will assign sides to the corresponding angles, making sure to identify the opposite side, adjacent side, and hypotenuse.

### Step 1: Identify sides based on angles
Let's assume:
- \( \angle T \) is at the vertex adjacent to side \( 24 \) (which we'll consider adjacent to \( T \)).
- Side opposite \( \angle T \) is \( 18 \) (this is the side opposite).
- The hypotenuse is \( 30 \) (the longest side).

### Step 2: Determine the sine and cosine ratios
Using the relationships of sine and cosine:
- **Sine** of an angle (\( \sin \)) is the ratio of the length of the opposite side to the length of the hypotenuse.
- **Cosine** of an angle (\( \cos \)) is the ratio of the length of the adjacent side to the length of the hypotenuse.

#### For \( \angle T \):
- Opposite side: 18
- Hypotenuse: 30
\[
\sin T = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{18}{30}
\]
Simplifying \( \frac{18}{30} \):
\[
\sin T = \frac{3}{5}
\]

#### For \( \angle U \):
- Adjacent side: 24
- Hypotenuse: 30
\[
\cos U = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{24}{30}
\]
Simplifying \( \frac{24}{30} \):
\[
\cos U = \frac{4}{5}
\]

### Final Answer
Thus, the simplified ratios are:
- \( \sin T = \frac{3}{5} \)
- \( \cos U = \frac{4}{5} \)