Question

1. a bird sits on top of a lamppost and spots a worm on the ground. the angle of depression from the bird to the worm is 35°. the distance from the bird to the worm is 25 meters. how tall is the lamppost to the nearest meter?

Explanation:

Step1: Understand the problem

We have a right triangle where the distance from the bird to the worm is the hypotenuse (25 meters), the height of the lamppost is the opposite side to the angle of depression (which is equal to the angle of elevation from the worm to the bird, \(35^\circ\)), and we need to find the height \(h\) of the lamppost. We can use the sine function, which is defined as \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\).

Step2: Apply the sine formula

Let \(\theta = 35^\circ\), hypotenuse \(= 25\) meters, and opposite side \(= h\) (height of the lamppost). So, \(\sin(35^\circ)=\frac{h}{25}\).

To solve for \(h\), we multiply both sides by 25: \(h = 25\times\sin(35^\circ)\).

Step3: Calculate the value

We know that \(\sin(35^\circ)\approx0.5736\) (using a calculator). Then \(h = 25\times0.5736 = 14.34\). Rounding to the nearest meter, we get \(h\approx14\) meters.

Answer:

The height of the lamppost is approximately \(\boxed{14}\) meters.