Given that triangle ABC has angle ABC = 90 degrees, AB = 6 cm and BC = 9 cm. Calculate the length of AC in cm to 1 decimal place

Mathematics

1 answer:

Luda [366]3 years ago

6 0

Answer:

AC = 6.7

Step-by-step explanation:

If this is a 90 degree triangle which I am assuming it is you would the Pythagorean theorem c^2 = a^2 + b^2 since bc seems long I am using that as the hypotenuse.

9^2 = 6^2 + b^2

81 = 36 + b^2

81-36 = b^2

45 = b^2

6.7 = b

so AC = 6.7

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Answer:

7 cm, 4.4 cm

Step-by-step explanation:

The side lengths can be found from the law of cosines. Each triangle has legs 3 cm and 5 cm. The angle between these will be 60° or 120°. Then the two sides of the parallelogram are ...

s = √(a² +b² -2ab·cos(C))

s = √(3² +5² -2·3·5·(±1/2)) = √(34 ±15) = {√49, √19}

The two side lengths are 7 cm and about 4.4 cm.