Determine 5324

An isosceles triangle with base c and arms a is given by: a = 50.3 cm c = 48.2 cm
Determine the interior angles and heights of the base c.

Correct answer:

h =  44.1507 cm
A =  61.3717 °
B =  61.3717 °
C =  57.2566 °

Step-by-step explanation:

$$\begin{gathered} a=50.3\text{cm} \\ c=48.2\text{cm} \\ h=\sqrt{a^2-(c/2{)}^2}=\sqrt{50.3^2-(48.2/2{)}^2}=44.1507\text{cm} \end{gathered}$$

$$\begin{gathered} A_1=\arcsin (h/a)=\arcsin (44.1507/50.3)\doteq 1.0711 \\ A=A_1\to \text{°}=A_1\cdot \frac{180}{\pi }\text{°}=1.0711\cdot \frac{180}{\pi }\text{°}=61.372\text{°}=61.3717^{\circ }=61°22^{\prime }18" \end{gathered}$$

$B=A=61.3717=61.3717^{\circ }=61°22^{\prime }18"$

$C=180-A-B=180-61.3717-61.3717=57.2566^{\circ }=57°15^{\prime }24"$

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