Right triangle

Ladder 16 feet reaches up 14 feet on a house wall. The 90-degree angle at the base of the house and wall. What are the other two angles or the length of the leg of the yard?

Correct answer:

b =  7.746 ft
A =  61.045 °
B =  28.955 °

Step-by-step explanation:

$$\begin{gathered} c=16\text{ ft } \\ a=14\text{ ft } \\ b=\sqrt{c^2-a^2}=\sqrt{16^2-14^2}=2\sqrt{15}=7.746\text{ ft} \end{gathered}$$

$$\begin{gathered} \sin A=a:c \\ A={\displaystyle \frac{180^{\circ }}{\pi }}\cdot \arcsin (a\mathrm{/}c)={\displaystyle \frac{180^{\circ }}{\pi }}\cdot \arcsin (14\mathrm{/}16)=61.045^{\circ }=61^{\circ }{2}^{\mathrm{\prime }}42\mathrm{"} \end{gathered}$$

$B=90-A=90-61.045=28.955^{\circ }=28^{\circ }57^{\mathrm{\prime }}18\mathrm{"}$

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