Question

57 which equation is correct? (a) triangle image with labels: hypotenuse 14 ft, angle at c 26°, side ab = x, side cb = y, right angle at b a $sin(26) = \frac{x}{14}$ b $sin(26) = \frac{14}{x}$ c $cos(26) = \frac{x}{14}$ d $cos(26) = \frac{14}{x}$ (b) solve for x (round to two decimals).

Explanation:

Part (a)

Step1: Recall SOHCAHTOA

In a right triangle, \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\), \(\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 26^\circ\), opposite side to \(26^\circ\) is \(x\), hypotenuse is \(14\).

Step2: Apply Sine Definition

So \(\sin(26^\circ)=\frac{x}{14}\), which matches option A.

Step1: Start with Correct Equation

From part (a), we have \(\sin(26^\circ)=\frac{x}{14}\).

Step2: Solve for \(x\)

Multiply both sides by \(14\): \(x = 14\times\sin(26^\circ)\). Calculate \(\sin(26^\circ)\approx0.4384\), then \(x\approx14\times0.4384\).

Step3: Compute the Value

\(14\times0.4384 = 6.1376\), round to two decimals: \(x\approx6.14\).

Answer:

A. \(\sin(26)=\frac{x}{14}\)

Part (b)