Thread: Trigonometry help please.....

Four rods, AB 20CM long, BC 22.5CM long, CD 25CM long and DA 27.5 long,
are pin-jointed at ABC and D. If the angle ABC is 120°, find

a. the distance AC

b. the angle ADC


thankyou

a)

Using cosine rule...

AC^2 = 20^2 + 22.5^2 - 2*20*22.5Cos120 = 1356.25

AC = 36.8 cm

b)

Again using cosine rule...

36.8^2 = 27.5^2 + 25^2 - 2*27.5*25CosADC

2*27.5*25CosADC = 27.5^2 + 25^2 - 36.8^2

ADC = Cos^-1((27.5^2 + 25^2 - 36.8^2)/(2*27.5*25)) = 90.0 degrees

Hello, sa87uk!

Four rods: AB 20cm long, BC 22.5cm long, CD 25cm long, and DA 27.5 cm long,
are jointed at A, B, C, D.

If the angle ABC is 120°, find

a) the distance AC
b) the angle ADC

Code:

                 22.5
          B o  *  *  *  o C
           * 120°    *    *
          *       *         *
      20 *     *              * 25
        *   *                   *
       * *                        *
    A o  *  *  *  *  *  *  *  *  *  o D
                   27.5

Law of Cosines: .

. .

(a) Therefore: . cm



Law of Cosines: .

.

(b) Therefore: .


Edit: Too fast for me, Sean!