Mathematics, 20.12.2019 10:31 dessy6546

Atriangle has sides with the following lengths: ab=3, bc=4, ca=5. which angle is the smallest?

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Answer from: saintsfan2004

A = 36.9°

Step-by-step explanation:

In this triangle we know the three sides:

AB = 3,

BC = 4 and

CA = 5.

Use The Law of Cosines first to find angle A first:

cos A = (BC² + CA² − AB²) / 2BCCA

cos A = (4² + 5² − 3²) / (2×4×5)

cos A = (16 + 25 − 9) / 40

cos A = 0.80

A = cos⁻¹(0.80)

A = 36.86989765°

A = 36.9° to one decimal place.

Next we will find another side. We use The Law of Cosines again, this time for angle B:

cos B = (CA² + AB² − BC²) / 2CAAB

cos B = (5² + 3² − 4²) / (2×5×3)

cos B = (25 + 9 − 16) / 30

cos B = 0.60

B = cos⁻¹(0.60)

B = 53.13010235°

B = 53.1° to one decimal place

Finally, we can find angle C by using 'angles of a triangle add to 180°:

C = 180° − 36.86989765° − 53.13010235°

C = 90°

Now we have completely solved the triangle i.e. we have found all its angles.

So we can analyze from above that the smallest angle in the triangle ABC is A with 36.9°.

Answer from: Quest

sine

step-by-step explanation:

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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