Question

How many different triangles of the same area can be drawn without changing the lengths of two sides?
I will make ypu as brainliest if you answer me correct in just 1 mins​

Answer 1

Answer:

If we use the formula for area = 1/2 ab sin C and the area and a and b are known, then we can use

sin C = 2 (area) / ab to find angle C as arcsin (2 (area) / ab) to constuct a triangle with that area and the given sides included in the angle. The actual length of the third side will take some figuring, probably with the law of cosines.

I am tempted to try this.

Let’s say the area is 100 square inches and the two sides are 20 inches and 30 inches. Then angle C will be arcsin (200 / 600) = approx 19.47 degrees

Then the length of the third side c can be found from

I t the remainder y. H0§utc = (400 + 900 - 1200 cos 19.47)^1/2 = approx 12.9854 inches.

We can use Heron’s formula to see if this is a teasonable answer.

If a=20 and b=30 and c=12.9854

s = approx 31.49

area = ((31.49) (11.49) (1.49) (18.5046))^½ = approx 99.88 square inches. Right on!! Pretty close to 100 square inches.

Answer 2

Answer:

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Step-by-step explanation:

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