Question

you measure your distance from a lamppost and the angle of elevation from the ground to the top of the lamppost. find the height of the lamppost.
( h ) in.
( 70^circ )
40 in.
the height of the lamppost is about inches.

Explanation:

Step1: Identify trigonometric ratio

We use the tangent function, since $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$, where $\theta=70^\circ$, opposite side is $h$, adjacent side is 40 in.

Step2: Set up the equation

$\tan(70^\circ) = \frac{h}{40}$

Step3: Solve for $h$

Rearrange to isolate $h$: $h = 40 \times \tan(70^\circ)$
Calculate $\tan(70^\circ) \approx 2.747$, so $h \approx 40 \times 2.747$

Answer:

The height of the lamppost is about 109.88 inches.