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mustafa455486a

12.05.2021

Mathematics

the missing side is , c= 22.1 and the missing angles are , ∠a= 36.7° and ∠b= 53.2° to the nearest tenth.

in the triangle abc, ∠c = 90°

the side opposite to ∠a is, a= 13.2 and side opposite to ∠b is, b= 17.7

according to the pythagorean theorem:

$c^2 = a^2 + b^2\\ \\ c^2 = (13.2)^2 + (17.7)^2 \\ \\ c^2 = 174.24 + 313.29 \\ \\ c^2 = 487.53$

⇒ c = 22.1 (taking square root on both sides)

for finding the missing angles, we will use the sine rule of triangle.

according to the sine rule:

$\frac{sina}{a}= \frac{sinb}{b}=\frac{sinc}{c}\\ \\ \frac{sina}{13.2}=\frac{sinb}{17.7}=\frac{sin90}{22.1} \\ \\ sina= \frac{13.2*sin90}{22.1}=\frac{13.2}{22.1} \\ \\ a= sin^-^1 (\frac{13.2}{22.1})=36. = 36.7 \\\\ \\ sinb =\frac{17.7*sin90}{22.1} =\frac{17.7}{22.1} \\ \\ b= sin^-^1(\frac{17.7}{22.1})= 53.=53.2$

so the missing side is , c= 22.1 and the missing angles are , ∠a= 36.7° and ∠b= 53.2° to the nearest tenth.

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