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Express tan JJ as a fraction in simplest terms.
H
I
J
8
10
Answer
Attempt 1 out of 2

answer that using this method
SOH CAH TOA
cos , K, equals, start fraction, adjacent, divided by, hypotenuse, end fraction
cos K=
hypotenuse
adjacent
​

We must find the hypotenuse.
We must find the hypotenuse.
Legs: 24 and 7, Hypotenuse: x
Legs: 24 and 7Hypotenuse: x
a, squared, plus, b, squared, equals, c, squared
a
2
+b
2
=
c
2

The Pythagorean Theorem
24, squared, plus, 7, squared, equals, x, squared
24
2
+7
2
=
x
2

Plug in. c is the hypotenuse.
576, plus, 49, equals, x, squared
576+49=
x
2

Square the numbers.
625, equals, x, squared
625=
x
2

Add
square root of, 625, end square root, equals, square root of, x, squared, end square root
625
​
=
x
2

​

Square root both sides.
25, equals, x
25=
x
Evaluate the square root.
cos , K, equals, start fraction, adjacent, divided by, hypotenuse, end fraction, equals, start fraction, 7, divided by, 25, end fraction, approximately equals, 0, point, 2, 8
cos K=
hypotenuse
adjacent
​
=
25
7
​
≈0.28

Answer 1

To find \(\tan JJ\) using the information provided, we can use the SOH CAH TOA method. First, we'll need to determine:

1. The lengths of the two legs adjacent and opposite to angle JJ.
2. Using these lengths, we can then find the tangent of angle JJ.

### Step 1: Identify the Legs
From the provided information:
- We have legs 24 and 7.
- Let's assume that:
- The leg measuring 24 is the opposite side of angle JJ.
- The leg measuring 7 is the adjacent side of angle JJ.

### Step 2: Use the Tangent Formula
Using the definition of tangent:
\[
\tan \theta = \frac{\text{opposite}}{\text{adjacent}}
\]
So for \(\tan JJ\):
\[
\tan JJ = \frac{24}{7}
\]

### Step 3: Simplify
The fraction \(\frac{24}{7}\) is already in simplest terms since 24 and 7 have no common factors (7 is a prime number and does not divide 24).

Thus, the final answer for \(\tan JJ\) in simplest terms is:
\[
\boxed{\frac{24}{7}}
\]