The perimeter of the triangle is about 136
Further explanation
Firstly , let us learn about trigonometry in mathematics.
Suppose the ΔABC is a right triangle and ∠A is 90°.
sin ∠A = opposite / hypotenuse
cos ∠A = adjacent / hypotenuse
tan ∠A = opposite / adjacent
There are several trigonometric identities that need to be recalled, i.e.
[tex]cosec ~ A = \frac{1}{sin ~ A}[/tex]
[tex]sec ~ A = \frac{1}{cos ~ A}[/tex]
[tex]cot ~ A = \frac{1}{tan ~ A}[/tex]
[tex]tan ~ A = \frac{sin ~ A}{cos ~ A}[/tex]
Let us now tackle the problem!
This problem is about Sine Rule.
First of all, we will calculate the ∠C :
∠A + ∠B + ∠C = 180°
72° + 16° + ∠C = 180°
∠C = 180° - 72° - 16°
∠C = 92°
Next, we will use the Sine Rule to find the length of the other side of the triangle.
[tex]\frac{c}{\sin \angle C} = \frac{b}{\sin \angle B}[/tex]
[tex]\frac{61}{\sin 92^o} = \frac{b}{\sin 16^o}[/tex]
[tex]b \approx \boxed {16.82}[/tex]
[tex]\frac{c}{\sin \angle C} = \frac{a}{\sin \angle A}[/tex]
[tex]\frac{61}{\sin 92^o} = \frac{a}{\sin 72^o}[/tex]
[tex]a \approx \boxed {58.05}[/tex]
Finally, we can find the perimeter of a triangle with the following formula
[tex]\text{Perimeter of the triangle} = a + b + c[/tex]
[tex]\text{Perimeter of the triangle} = 58.05 + 16.82 + 61[/tex]
[tex]\text{Perimeter of the triangle} \approx \boxed {136}[/tex]
Learn more
- Calculate Angle in Triangle : https://brainly.com/question/12438587
- Periodic Functions and Trigonometry : https://brainly.com/question/9718382
- Trigonometry Formula : https://brainly.com/question/12668178
Answer details
Grade: College
Subject: Mathematics
Chapter: Trigonometry
Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse
