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.
whats the answer
To solve this problem, we can use the concept of similar triangles. Let's assume that Dakota's height is represented by "h" inches.
When the sun's rays are at an angle of 39°, the angle of elevation from Dakota's head to the sun is also 39°. This forms a right triangle with the height of Dakota being the opposite side, and the length of the shadow being the adjacent side.
Using the tangent function, we can set up the following equation:
tan(39°) = h / 77
To solve for h, we can cross multiply and then divide by tan(39°):
h = tan(39°) * 77
Using a calculator, we find:
h ≈ 77 * 0.809
h ≈ 62.45
Therefore, Dakota's height is approximately 62.45 inches. Rounded to the nearest inch, Dakota is about 62 inches tall.
To find Dakota's height, we can use a trigonometric ratio called tangent. The tangent of an angle is equal to the length of the opposite side divided by the length of the adjacent side. In this case, the angle is 39°, and the opposite side is Dakota's height, while the adjacent side is the length of her shadow.
Let's denote Dakota's height as x and the length of her shadow as y. According to the given information, we know that the angle of elevation from the sun is 39° (which is referred to as the angle between the sun's rays and the vertical).
Using the tangent function, we can set up the following equation:
tan(39°) = x / y
Now, we can rearrange the equation to solve for x:
x = y * tan(39°)
We are given that the length of Dakota's shadow is 77 inches. Plugging this value into the equation, we get:
x = 77 * tan(39°)
Calculating the value on the right-hand side:
x ≈ 77 * 0.809784 = 62.372
Therefore, Dakota's height is approximately 62 inches when rounded to the nearest inch.
looks like
sin39° = height/77
height = 77sin39° = ...