Calculate ac. round to the nearest hundredth.

Length of AC is 13.19 cm

Step-by-step explanation:

We have the right triangle ADB with an angle 65° and the length of hypotenuse = 7 cm.

As we know, 'In a right angled triangle, the angles and sides can be written in trigonometric forms'.

That is,

i.e.

i.e

i.e

i.e. AD = 3 cm

Also, Pythagoras Theorem' states that 'The sum of squares of the length of the sides in a right triangle is equal to the square of the length of the hypotenuse'.

That is,

i.e.

i.e.

i.e.

i.e.

i.e.

i.e.

Since, length of a side cannot be negative.

So, BD = 6.33 cm

Again using Pythagoras Theorem for the right triangle BDC, we have,

i.e.

i.e.

i.e.

i.e.

i.e.

Since, length of a side cannot be negative.

So, DC = 10.194 cm.

Finally, as the side AC is the sum of segments AD and DC, we have,

AC = AD + DC

i.e. AC = 3 + 10.194

i.e. AC = 13.19 cm

Hence, the length of AC is 13.19 cm.

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step-by-step explanation: