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 Pythagoras theorem

For the ladder - tree problem: In a right - triangle (formed by the tree, ground, and ladder), if \(a = 30\) (base), \(b=40\) (height), and \(c\) is the hypotenuse (length of the ladder). By Pythagoras theorem \(c^{2}=a^{2}+b^{2}\).

$$c^{2}=30^{2}+40^{2}$$

$$c^{2}=900 + 1600$$

$$c^{2}=2500$$

$$c=\sqrt{2500}=50$$

For the TV - screen problem: Let the length \(l = 20\), diagonal \(d = 25\), and width \(w=x\). Using Pythagoras theorem \(d^{2}=l^{2}+w^{2}\), so \(w^{2}=d^{2}-l^{2}\)

$$x^{2}=25^{2}-20^{2}$$

$$x^{2}=625-400$$

$$x^{2}=225$$

$$x = 15$$

Answer:

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