Answer:
h = 10.9 ft (nearest tenth)
Explanation:
Given:
the longest side (ladder) = 12 ft
Distance from the base of the tree to the foot of the ladder = 5ft
To find:
the distance from the base of the tree to the top of the tree where the cat is located
We will be using Pythagoras theorem as the ladder and tree form a right-angled triangle
Hypotenuse² = opposite² + adjacent²
hyp = 12 ft, opp = h ft, adj = 5 ft
substitute the values:
[tex]\begin{gathered} 12^2\text{ = h}^2+\text{ 5}^2 \\ 144\text{ = h}^2\text{ + 25} \\ \\ substract\text{ 25 from both sides:} \\ 144\text{ - 25 = h}^2 \end{gathered}[/tex][tex]\begin{gathered} 119\text{ = h}^2 \\ \\ square\text{ root both sides:} \\ h\text{ = }\sqrt{119} \\ h\text{ = 10.9 ft} \end{gathered}[/tex]
