Mathematics, 28.01.2020 00:31, neariah24

Determine if there are zero, one, or two triangles for the following:

Answers: 3

Show answers

Answers

Given the data of the sides and the included angle, it can be said that there exist two triangles. Since a is greater than (b sin A), therefore there are two solutions or two triangles in the given measures.

answered: daydallas01

Answer with explanation:

In Δ ABC

m ∠A=48°

a=10 m

b=12 m

Using Sine Law

$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\\\\\frac{10}{\sin 48^{\circ}}=\frac{12}{\sin B}\\\\ \ sinB^{\circ}=\frac{12 \times \sin 48^{\circ}}{10}\\\\\ sinB^{\circ}=\frac{12 \times 0.7431}{10}\\\\\ sinB^{\circ}=0.9\\\\B=65^{\circ}$

So, Angle C can be obtained by using angle sum property of triangle.

So,This is one kind of triangle, having measure of three Angles are , 48°, 65°,67°.

≡≡Now, we will use cosine law to find if there is another triangle having measure of one angle 48°.

$\cos 48^{\circ}=\frac{12^2+c^2-10^2}{2 \times 12 \times c}\\\\0.67=\frac{144+c^2-100}{24 c}\\\\16.08 c=44+c^2\\\\100 c^2 -1608 c +4400=0\\\\25 c^2-402 c+1100=0\\\\c=12.58\\\\c=3.50$

Sum of two sides of triangle should always be greater than third side.

So, c=3.50

and, c= 12.58

Triangle of two type is possible having dimension, a=10 m, b=12 m, c=12.58 m and a=10 m, b=12 m, c=3.50 m.

But,when side c=12.58 m, then ∠C=67°.

So, There are two triangles possible in this case,out of which one is Congruent with triangle obtained in case 1.

So,There are two distinct Triangles.

⇒⇒⇒Two Triangles

answered: Guest

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction: this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology: the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion: the last is the discussion, this can be either by management people or persons who are all interested , etc.

answered: Guest

drive more conversions to your website

conversions are the outcome of your efforts. when a visitor sign up for any newspaper, or fill any form to order a specific product or when your page is shared on social media, all such attempts mean conversions of a website. whenever your desired action is fulfilled, the conversion rate of your website will increase. this increase in your conversion rate will prove that your website is going well. it also confirms that the quality of your website’s marketing was really good.drive more conversion to your website drive more conversions to your website