Question

question 2
20 pts
a ladder leaning against a wall makes an angle of 70° with the ground. if the ladder is 12 feet long, how high on the wall is the ladder? round to the nearest tenth if necessary.

Explanation:

Step1: Identify the trig - function

We use the sine function since $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 70^{\circ}$, the hypotenuse is the length of the ladder ($c = 12$ feet), and the opposite side is the height on the wall ($h$).

Step2: Set up the equation

$\sin(70^{\circ})=\frac{h}{12}$.

Step3: Solve for $h$

$h = 12\times\sin(70^{\circ})$.
Since $\sin(70^{\circ})\approx0.9397$, then $h=12\times0.9397 = 11.2764\approx11.3$ feet.

Answer:

11.3 feet