Question

teacher
dfa1.8.m.g.b.07 apply the pythagorean theorem to determine unknown side
lengths in right triangles in real - world context and mathematical problems in two
and three dimensions./5

1. a firefighter is placing a 15 - foot ladder against a house. he places the ladder 10 feet

away from the house. how high up the house will he be able to reach? round to the
nearest foot.
a. 10 feet
b. 11 feet
c. 18 feet
d. 25 feet

1. a youth soccer field is 24 yards long and 10 yards wide. the team practicing on the

field is told to run the diagonal of the field. how far did they run?
a. 14 yards
b. 16 yards
c. 24 yards
d. 26 yards

1. there is a fire lookout tower at point a and a second one at point b. the lookout

towers are 5 miles apart. if tower a spots a fire at a distance of 8 miles away, how far
is the fire from tower b? round to the nearest tenths place.
a. 5.1 miles
b. 6.2 miles
c. 9.4 miles
d. 10.1 miles

Explanation:

Step1: Apply Pythagorean Theorem for problem 1

The Pythagorean Theorem is \(a^{2}+b^{2}=c^{2}\). Here, the ladder is the hypotenuse \(c = 15\) feet and the base \(a=10\) feet. We need to find \(b\).

$$b=\sqrt{c^{2}-a^{2}}=\sqrt{15^{2}-10^{2}}=\sqrt{225 - 100}=\sqrt{125}\approx11$$

Step2: Apply Pythagorean Theorem for problem 2

The length \(a = 24\) yards and width \(b = 10\) yards. The diagonal \(c\) (using \(a^{2}+b^{2}=c^{2}\)):

$$c=\sqrt{24^{2}+10^{2}}=\sqrt{576+100}=\sqrt{676}=26$$

Step3: Apply Pythagorean Theorem for problem 3

The distance between towers \(a = 5\) miles and from tower A to fire \(b = 8\) miles. The distance from tower B to fire \(c\) (using \(a^{2}+b^{2}=c^{2}\)):

$$c=\sqrt{5^{2}+8^{2}}=\sqrt{25 + 64}=\sqrt{89}\approx9.4$$

Answer:

1. B. 11 feet
2. D. 26 yards
3. C. 9.4 miles