Mathematics, 04.08.2019 06:50 mjam85877

Three security cameras were mounted at the corners of a triangular parking lot. camera 1 was 158 ft from camera 2, which was 121 ft from camera 3. cameras 1 and 3 were 140 ft apart. which camera had to cover the greatest angle?

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This is a good exercise to apply the law of cosines and the law of sines:
First, we are going to use the law of cosines to find any angle, and then we can use the law of sines to find the other one; last but not least we are going to use the internal angles definition (the sum of the interior angles of a triangle is 180°) to fin our final angle and compare them:

Using the law of cosines: we know that $COSA= \frac{b^{2}+ c^{2}- a^{2} }{2bc}$ , but we need the vale of the angle A, so we are going to use the inverse cosine function, ARCCOS, to solve for A:
$A=ARCCOS(\frac{b^{2}+ c^{2}- a^{2} }{2bc})$
We also know that a=121, b=140, and c=158, so the only thing we have to do is replace the values into our equation:
$A=ARCCOS(\frac{140^{2}+ 158^{2}- 121^{2} }{2(140)(158)})$
$A=ARCCOS( \frac{29923}{44240})$
A=47.4

°

Now that we know the value of the angle A, we can use the law of sines to find the angle B:
$\frac{SinA}{a} = \frac{SinB}{b}$
$SinB= \frac{bSinA}{a}$
And just like before we'll use the inverse sine function, ARCSIN, to solve for B:
$B:ARCSin( \frac{bSinA}{a} )$
We know that b=140, a=121, and A=47.4, so we can replace the vales to get:
$B=ARCSin( \frac{140Sin(47.4)}{121} )$
B=58.4

°

Now that we have two angles, we can use the interior angle definition. If the sum of the interiors angle of a triangle is 180°, then:
C=180-(A+B)

We can conclude that the camera that has to cover the greatest angle is camera 3, and it has to cover an angle of 74.2°.

Three security cameras were mounted at the corners of a triangular parking lot. camera 1 was 158 ft

Three security cameras were mounted at the corners of a triangular parking lot. camera 1 was 158 ft

Answer from: Quest

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc

Answer from: Quest

i don't think there is enough

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