Question

a 17-ft ladder leans against a building so that the angle between the ground and the ladder is $77^{\circ}$.
how high does the ladder reach on the building? round to the hundredths. (2 decimal places)

Explanation:

Step1: Identify trigonometric ratio

We use the sine function, since $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$, where the opposite side is the height we need, and the hypotenuse is the ladder length.

Step2: Plug in known values

Let $h$ = height on the building. $\theta = 77^\circ$, hypotenuse = 17 ft.
$\sin(77^\circ) = \frac{h}{17}$

Step3: Solve for $h$

Rearrange to isolate $h$: $h = 17 \times \sin(77^\circ)$
Calculate $\sin(77^\circ) \approx 0.97437$, so $h \approx 17 \times 0.97437$

Step4: Compute and round

$h \approx 16.56429$, rounded to two decimals is $16.56$

Answer:

16.56 ft