Question

solve for x. round your answer to the nearest tenth.

x = m

(see yellow hint below.)

show your work

hints

1. sin ∠ = \frac{opposite}{hypotenuse}

cos ∠ = \frac{adjacent}{hypotenuse}

tan ∠ = \frac{opposite}{adjacent}

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, for an angle of \(31^{\circ}\), the side opposite to the angle is \(11\) m and the hypotenuse is \(x\). We use the sine ratio: \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 31^{\circ}\), opposite \(= 11\) m, and hypotenuse \(=x\). So, \(\sin31^{\circ}=\frac{11}{x}\).

Step2: Solve for \(x\)

We can rewrite the equation \(\sin31^{\circ}=\frac{11}{x}\) as \(x=\frac{11}{\sin31^{\circ}}\).
We know that \(\sin31^{\circ}\approx0.515\). Then \(x=\frac{11}{0.515}\approx21.4\).

Answer:

\(21.4\)