Question

1. for an acute angle θ, the equation sin(θ) = cos(25°) is true. (hint: think about #3 above...)

a. what is the value of θ?
b. draw a picture of the right triangle.

Explanation:

Step1: Use co-function identity

Recall $\sin(\theta) = \cos(90^\circ - \theta)$

Step2: Set up equation for $\theta$

Given $\sin(\theta) = \cos(25^\circ)$, so $90^\circ - \theta = 25^\circ$

Step3: Solve for $\theta$

$\theta = 90^\circ - 25^\circ = 65^\circ$

Step4: Describe right triangle

Right triangle has acute angles $25^\circ$ and $65^\circ$, right angle $90^\circ$. Label: angle $\theta=65^\circ$, its opposite side corresponds to the adjacent side of the $25^\circ$ angle, hypotenuse is longest side.

Answer:

a. $\boldsymbol{65^\circ}$
b. A right triangle with one right angle ($90^\circ$), one acute angle of $65^\circ$ (labeled $\theta$), and the other acute angle of $25^\circ$. The side opposite the $65^\circ$ angle is adjacent to the $25^\circ$ angle, and the hypotenuse is the side opposite the right angle.