The ladder and wall

A 6.5-meter-long ladder rests against a vertical wall. Its lower end rests on the ground 1.6 meters from the wall. Determine how high the top of the ladder reaches and at what angle it rests against the wall.

Final Answer:

h =  6.3 m
α =  75.75 °

Step-by-step explanation:

$$\begin{gathered} c=6.5\text{m} \\ a=1.6\text{m} \\ {c}^2=a^2+h^2 \\ h=\sqrt{c^2-a^2}=\sqrt{6.5^2-1.6^2}=6.3\text{m} \end{gathered}$$

$$\begin{gathered} \tan \alpha =h:a \\ A=\arctan (h/a)=\arctan (6.3/1.6)\doteq 1.3221\text{rad} \\ \alpha =A\to \text{°}=A\cdot \frac{180}{\pi }\text{°}=1.3221\cdot \frac{180}{\pi }\text{°}=75.75\text{°}=75.75^{\circ }=75°45^{\prime } \end{gathered}$$

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