Question

3.

angle (θ)	opposite	adjacent	hypotenuse	trig function

(the triangle at the bottom has a right angle at c, angle at b is 37°, side bc is 11, side ab is x, and vertex a is at the top right of the right angle.)

Explanation:

Step1: Identify sides relative to angle B

In right triangle \( \triangle ABC \) with right angle at \( C \), for angle \( B = 37^\circ \):

• Adjacent side to \( 37^\circ \) is \( BC = 11 \)
• Hypotenuse is \( AB = x \)
• We use cosine function: \( \cos(\theta)=\frac{\text{Adjacent}}{\text{Hypotenuse}} \)

Step2: Set up the equation

\( \cos(37^\circ)=\frac{11}{x} \)

Step3: Solve for \( x \)

Rearrange the equation: \( x = \frac{11}{\cos(37^\circ)} \)
Using \( \cos(37^\circ)\approx0.8 \) (approximate value for common trigonometric ratios in right triangles):
\( x=\frac{11}{0.8}=13.75 \) (If using more precise value of \( \cos(37^\circ)\approx0.7986 \), \( x=\frac{11}{0.7986}\approx13.77 \))

Answer:

\( x\approx13.75 \) (or \( \approx13.77 \) with more precise \( \cos(37^\circ) \))