Question

a ladder rests against a tree. if it reaches a height of 40 m from the ground, and if the distance between the foot of the ladder and the tree is 30 m, then the length of the ladder is ___ m. problem 4. a tv screen is 20 inches long. if the diagonal measures 25 inches, how long is the width of the tv

Explanation:

Step1: Apply Pythagorean theorem

For the ladder - tree problem, let the length of the ladder be \(x\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 30\), \(b=40\) and \(c=x\). So \(x^{2}=30^{2}+40^{2}\).

Step2: Calculate \(30^{2}+40^{2}\)

\(30^{2}=900\), \(40^{2}=1600\). Then \(30^{2}+40^{2}=900 + 1600=2500\).

Step3: Find \(x\)

Since \(x^{2}=2500\), then \(x=\sqrt{2500}\). And \(\sqrt{2500}=50\).

For the TV - screen problem, let the width be \(x\). Using the Pythagorean theorem \(x^{2}+20^{2}=25^{2}\).

Step1: Rearrange the formula

\(x^{2}=25^{2}-20^{2}\).

Step2: Calculate \(25^{2}-20^{2}\)

\(25^{2}=625\), \(20^{2}=400\). So \(25^{2}-20^{2}=625 - 400 = 225\).

Step3: Find \(x\)

Since \(x^{2}=225\), then \(x=\sqrt{225}\). And \(\sqrt{225}=15\).

Answer:

The length of the ladder is \(50\) m. The width of the TV is \(15\) inches.