Question

Some of the measurements of right triangle
K
S
N
KSN are shown.



m
∠
S
N
K
=
90
°
,
m
∠
K
S
N
=
θ
°
,

S
N
=
65
,
m∠SNK=90°, m∠KSN=θ°, SN=65, and
K
S
=
97.
KS=97.





A relationship that can be used to determine the value of
θ
θ, in degrees, is
sin(θ) = 65/97
.



The value of
θ
θ is approximately
48
degrees.

Answer 1

To determine the angle \( \theta \) in triangle \( KSN \) given that \( \sin(\theta) = \frac{65}{97} \), you can use the inverse sine function. Here’s how you can do that:

1. Given:
- \( \sin(\theta) = \frac{65}{97} \)

2. To find \( \theta \), use the inverse sine function:
\[
\theta = \sin^{-1}\left(\frac{65}{97}\right)
\]

3. Calculating \( \sin^{-1}\left(\frac{65}{97}\right) \):

You can use a calculator to find this value.

- When you calculate \( \sin^{-1}\left(\frac{65}{97}\right) \), you should get approximately \( 48.37^\circ \).

So, rounding to the nearest whole degree gives:
\[
\theta \approx 48^\circ
\]

Therefore, you can conclude that the value of \( \theta \) is approximately **48 degrees**, which matches the statement you provided.