Dmitri has let out 40 m of his kite string, which makes an angle of 72° with the horizontal ground. Show complete working for all answers.  a. Find the height of the kite, to the nearest metre.b. Suppose the Sun is shining directly above the kite. How far is the kite’s shadow from Dmitri, to the nearest metre?

a. To find the height of the kite, we can use the sine of the angle. The sine of an angle in a right triangle is defined as the length of the opposite side (the height in this case) divided by the length of the hypotenuse (the kite string in this case). So, we have:

sin(72°) = height / 40m

To find the height, we rearrange the equation to solve for height:

height = sin(72°) * 40m

Using a calculator, sin(72°) is approximately 0.9511. So:

height = 0.9511 * 40m = 38.044m

Rounding to the nearest meter, the height of the kite is 38m.

b. To find the distance of the kite's shadow from Dmitri, we can use the cosine of the angle. The cosine of an angle in a right triangle is defined as the length of the adjacent side (the shadow in this case) divided by the length of the hypotenuse (the kite string in this case). So, we have:

cos(72°) = shadow / 40m

To find the shadow, we rearrange the equation to solve for shadow:

shadow = cos(72°) * 40m

Using a calculator, cos(72°) is approximately 0.3090. So:

shadow = 0.3090 * 40m = 12.36m

Rounding to the nearest meter, the distance of the kite's shadow from Dmitri is 12m.