Mathematics: Find the perimeter of each of the two noncongruent triangles where a = 15, b = 20, and a = 29°

Mark these points on the graph to form a right angled triangle.Angle Y will be 90 degrees...

Find the perimeter of each of the two noncongruent

Ответ:

yesharabaskoro

09.03.2022

Mathematics

Answer with explanation:

Using Sine Rule for Congruence of Triangles

$\Rightarrow\frac{a}{\ SinA}=\frac{b}{\ Sin B}=\frac{c}{\ Sin C}\\\\\Rightarrow\frac{15}{\ Sin29^{\circ}}=\frac{20}{\ Sin B}\\\\\Rightarrow\frac{15}{0.49}=\frac{20}{\ Sin B}\\\\\Rightarrow \ SinB=\frac{20 \times 0.49}{15}\\\\\Rightarrow \ SinB=\frac{9.8}{15}\\\\\Rightarrow \ SinB=0.65\\\\B=41^{\circ}$

Using Angle Sum Property of Triangle

⇒∠A+∠B+∠C=180°

⇒29°+41°+∠C=180°

⇒∠C=180°-70°

⇒∠C=110°

→Again Using Sine Rule

$\Rightarrow \frac{b}{\ Sin B}=\frac{c}{\ Sin C}\\\\\Rightarrow \frac{20}{\ Sin 41^{\circ}}=\frac{c}{\ Sin 110^{\circ}}\\\\\Rightarrow \frac{20}{0.65}=\frac{c}{0.94}\\\\\Rightarrow \frac{20 \times 0.94}{0.65}=c\\\\\Rightarrow c=\frac{18.8}{0.65}\\\\\Rightarrow c=28.92$

Length of third Side =28.92 unit

So,Perimeter of Triangle

=Sum of sides of triangle

=a +b +c

=15 + 20 +28.92

= 63.92 unit

0,0(0 оценок)

Find the perimeter of each of the two noncongruent triangles where a = 15, b = 20, and a = 29°

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question