Question

at what angle, in degrees, should the agent shoot his laser gun? round your final answer to the nearest tenth.

Explanation:

Step1: Identify the triangle type

We have a right triangle where the opposite side to the angle \( \theta \) is \( 324 \) and the adjacent side is \( 54 \). We can use the tangent function, which is defined as \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \).

Step2: Calculate the tangent of the angle

Substitute the values into the tangent formula: \( \tan(\theta)=\frac{324}{54} = 6 \).

Step3: Find the angle

To find \( \theta \), we take the arctangent (inverse tangent) of \( 6 \). So \( \theta=\arctan(6) \). Using a calculator, \( \arctan(6)\approx 80.5^\circ \) (rounded to the nearest tenth).

Answer:

\( 80.5 \)