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Calculate AC. Round to the nearest hundredth.

Calculate AC. Round to the nearest hundredth.-example-1

1 Answer

7 votes

Answer:

Length of AC is 13.19 cm

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,
\cos x=(Base)/(Hypotenuse)

i.e.
\cos 65=(AD)/(7)

i.e
AD=7* \cos 65

i.e
AD=7* 0.4226

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,
hypotenuse^(2)=perpendicular^(2)+base^(2)

i.e.
AB^(2)=BD^(2)+AD^(2)

i.e.
BD^(2)=AB^(2)-AD^(2)

i.e.
BD^(2)=7^(2)-3^(2)

i.e.
BD^(2)=49-9

i.e.
BD^(2)=40

i.e.
BD=\pm 6.33

Since, length of a side cannot be negative.

So, BD = 6.33 cm

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


BC^(2)=BD^(2)+DC^(2)

i.e.
BC^(2)-BD^(2)=DC^(2)

i.e.
12^(2)-6.33^(2)=DC^(2)

i.e.
DC^(2)=144-40.07

i.e.
DC^(2)=103.93

i.e.
DC=\pm 10.194

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.

User Ivo Van Der Wijk
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