Question

a) Use the lengths labelled on triangle X to write the value of sin 64.2° as a fraction. b) Show that working out sin 64.2° using the lengths given on triangle Y gives a fraction with the same value as the one found in part a). X 9 cm shown below. 64.2° 10 cm Y 18 cm 64.2°​

Answer 1

a) The value of sin 64.2° as a fraction using triangle X is 9/10. b) Using the lengths on triangle Y gives the same value of 2/3 for sin 64.2°.

Step-by-step explanation:

a) Use the lengths labelled on triangle X to write the value of sin 64.2° as a fraction:

To find the value of sin 64.2°, we will use the lengths of the sides in triangle X. Since sin is equal to the ratio of the length of the side opposite the angle to the hypotenuse, we can write sin 64.2° as:

sin 64.2° = opposite/hypotenuse = 9 cm/10 cm = 9/10 = 9/10

b) Show that working out sin 64.2° using the lengths given on triangle Y gives a fraction with the same value:

To find the value of sin 64.2° using the lengths on triangle Y, we can follow the same process. Since sin is equal to the ratio of the length of the side opposite the angle to the hypotenuse, we can write sin 64.2° as:

sin 64.2° = opposite/hypotenuse = 18 cm/27 cm = 18/27 = 6/9 = 2/3

Both fractions, 9/10 and 2/3, have the same value, showing that the lengths given on triangle Y also result in the same value of sin 64.2°.