find y. round to the nearest tenth: y = ?ft

Explanation:

Step1: Identify the trigonometric ratio

We use the tangent function since $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here $\theta = 31^{\circ}$, the opposite - side to the angle is $y$ and the adjacent - side is $400$ ft. So $\tan31^{\circ}=\frac{y}{400}$.

Step2: Solve for $y$

Multiply both sides of the equation $\tan31^{\circ}=\frac{y}{400}$ by $400$. We know that $\tan31^{\circ}\approx0.60086$. Then $y = 400\times\tan31^{\circ}$. $y=400\times0.60086 = 240.344$.

Step3: Round the result

Rounding $240.344$ to the nearest tenth gives $y\approx240.3$.

Answer:

$240.3$