Question

a 35 - ft ladder leans against a wall making a 70° angle with the ground. how high does the ladder reach on the wall? round your answers to the nearest tenth of a foot. feet

Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle where the ladder is the hypotenuse ($c = 35$ ft) and the height on the wall is the side opposite the given angle ($\theta=70^{\circ}$). We use the sine function: $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.
So, $\sin(70^{\circ})=\frac{h}{35}$, where $h$ is the height on the wall.

Step2: Solve for $h$

Multiply both sides of the equation by 35: $h = 35\times\sin(70^{\circ})$.
We know that $\sin(70^{\circ})\approx0.9397$.
Then $h = 35\times0.9397=32.8895$.

Answer:

$32.9$ feet