Question

using trig to find a side
using trig to find angles
trig word problems (diagram given)
level 1
trig identity opposite / adjacent /
scientific calculator
graphing calculator
answer
attempt 1 out of 2
x =
submit

Explanation:

Step1: Identify the trigonometric function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 42^{\circ}\), the hypotenuse \(OQ = 5\), and the opposite side to the angle \(42^{\circ}\) is \(OP=x\).

Step2: Set up the equation

Using the sine formula \(\sin(42^{\circ})=\frac{x}{5}\).

Step3: Solve for \(x\)

Multiply both sides of the equation by \(5\): \(x = 5\times\sin(42^{\circ})\).
Using a calculator, \(\sin(42^{\circ})\approx0.6691\). Then \(x = 5\times0.6691=3.3455\approx3.35\)

Answer:

\(3.35\)