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Question

A right triangle shows the hypotenuse labeled c, a leg labeled a, and a leg labeled b. The sides a and c form an angle phi, the sides a and b form a right angle, and the sides c and b form an angle theta.

If c=17 in. and b=15 in. , find the value of sinθ . Write your answer as a fraction. You do not need to simplify.

Answer 1

To find \( \sin \theta \) in a right triangle, we can use the definition of sine in relation to the triangle's sides. Specifically,

\[ \sin \theta = \frac{\text{opposite side}}{\text{hypotenuse}} \]

In this case, \( \theta \) is the angle opposite side \( b \). Here, the opposite side to \( \theta \) is \( b \), and the hypotenuse is \( c \).

Given the values:

• \( c = 17 \) in (hypotenuse)
• \( b = 15 \) in (opposite side to angle \( \theta \))

We can substitute these values into the sine formula:

\[ \sin \theta = \frac{b}{c} = \frac{15}{17} \]

Thus, the value of \( \sin \theta \) is:

\[ \sin \theta = \frac{15}{17} \]