Question

1. gwendolyn placed a 10 - foot ladder against the side of her house so that the base of the ladder was 3 feet from the base of the house, as shown in the diagram below. which measurement in feet is closest to d, the distance from the top of the ladder to the ground? a2 + b2 = c2 f 10.4 ft g 7.0 ft h 6.5 ft j 9.5 ft 12. the drawing below shows a side view of a picture frame on marys desk.

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse (length of the ladder, $c = 10$ feet) and $a$ is the distance from the base of the house to the base of the ladder ($a = 3$ feet), and $b=d$ (the height we want to find). Rearranging for $b$, we get $b=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

Substitute $c = 10$ and $a = 3$ into the formula: $d=\sqrt{10^{2}-3^{2}}=\sqrt{100 - 9}=\sqrt{91}$.

Step3: Calculate the value

$\sqrt{91}\approx9.54$ feet.

Answer:

J. 9.5 ft