Mathematics, 21.09.2019 23:30 ReaLily

In ∆abc, m∠a = 60º, m∠c = 30º, and ab = 6 inches. what is the length of side bc?

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ABC is a 30 60 90 triangle
In such a triangle, the shortest side AB multiplied by the square root of 3 equals the length of the "medium" side CB.
6 * sq root (3) = 10.39
(Incidentally, the hypotenuse AC = short side*2 = 12)

In ∆abc, m∠a = 60º, m∠c = 30º, and ab = 6 inches. what is the length of side bc?

In ∆abc, m∠a = 60º, m∠c = 30º, and ab = 6 inches. what is the length of side bc?

Answer from: aquinomoises518

$6\sqrt{3}\approx 10.39$ inches.

Step-by-step explanation:

We have been given that in ∆ABC, $m\angle A=60^{\circ}$ , $m\angle C=30^{\circ}$ , and the length of segment AB is 6 inches. We are asked to find the length of side BC.

We can see from our attachment that in ∆ABC, the side BC is opposite side and side AB is the adjacent side for the angle A.

Since tangent relates the opposite side of a right triangle with hypotenuse, so we can set an equation to find the length of side BC as:

$\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}$

$\text{tan}(60^{\circ})=\frac{\text{BC}}{6}$

$\sqrt{3}=\frac{\text{BC}}{6}$

$\sqrt{3}\times 6=\frac{\text{BC}}{6}\times 6$

$6\sqrt{3}=\text{BC}$

$\text{BC}\approx 10.39$

Therefore, the length of side BC is $6\sqrt{3}\approx 10.39$ inches.

Answer from: Quest

The variables should add up to equal 1

Answer from: Quest

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.

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Mathematics, 21.06.2019 22:30