Answer:
54.3° (first choice)
Step-by-step explanation:
The given figure is a right triangle with hypotenuse 32 and base (b) = 26
We will use the law of sines to solve for the missing value of [tex]\theta[/tex]
Law of Sines
The Law of Sines, also known as the Sine Rule, is a fundamental concept in trigonometry. It provides a relationship between the sides and angles of an oblique triangle (a triangle that is not a right triangle). Let’s dive into the details:
The Law of Sines states that for any triangle, the ratio of a side length to the sine of the opposite angle is equal for all three sides:
[tex]\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}[/tex]
Here, a, b, and c represent the side lengths, and (A), (B), and (C) denote the corresponding angles.
In other words, the sine of an angle divided by the length of the side opposite that angle is constant for all three pairs of angles and sides.
Applying the law of sines to the given triangle we get
[tex]\dfrac{32}{\sin 90} = \dfrac{26}{\sin \theta}\\\\\sin 90 = 1\\\\\implies 32 = \dfrac{26}{\sin \theta}[/tex]
Cross multiplying we get
[tex]\sin \theta = \dfrac{26}{32} = 0.8125\\\\\theta = sin^{-1}(0.8125) = 54.3^\circ[/tex]
