Question

5.2 part 2
score: 7/10 answered: 7/10
question 8
a 24 foot ladder leans against a building so that the angle between the ground and the ladder is 70°. how high does the ladder reach up the side of the building? round to 2 decimal places.
feet
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Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle where the ladder is the hypotenuse ($c = 24$ feet) and the height on the building is the side opposite the given angle ($\theta=70^{\circ}$). We use the sine function: $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Let $h$ be the height. So, $\sin(70^{\circ})=\frac{h}{24}$.

Step2: Solve for $h$

Multiply both sides of the equation by 24: $h = 24\times\sin(70^{\circ})$.
We know that $\sin(70^{\circ})\approx0.9397$. Then $h = 24\times0.9397$.
$h=22.5528$.

Answer:

$22.55$