Question

When the sun’s rays are at an angle of 39°, the distance from the top of Dakota’s head to the tip of her shadow is 77 inches. About how tall is Dakota? Round your answer to the nearest inch if necessary.

Answer 1

Answer:

Dakota is 48 inches tall.

Explanation:

We can solve this problem using trigonometry. Since the angle between Dakota and the ground is nearly 90°, we can construct a rectangle triangle, whose sides are Dakota, her shadow, and the distance between the top of her head to the tip of her shadow. Let the Dakota's height be D. Since the angle between the sun's rays and the ground is 39° and the distance between the tip of her shadow and Dakota's head is 77 inches, we can state that:

$\sin39\°=\frac{D}{77"}\\\\\implies D=77"\sin39\°\\\\D=48"$

So, this means that Dakota is 48 inches tall.