Standing on level ground, a person casts a shadow 1.41 m long when the Sun is 34.7 degrees above the horizon. How tall is the person? Give your answer in meters.
h = 1.41 tan(34.7º)
To find the height of the person, we can use the concept of similar triangles. Let's consider the situation:
Let the height of the person be "h" and the length of the shadow be "s".
We have a right triangle formed by the person, the length of their shadow, and the line connecting the person's head to the tip of the shadow.
The angle between the ground and the line connecting the person's head to the tip of the shadow is 90 degrees minus the angle of elevation of the Sun, which is 90 - 34.7 = 55.3 degrees.
Using the property of similar triangles, we can set up the following proportion:
h / s = tan(angle)
where "angle" is the angle of elevation between the ground and the line connecting the person's head to the tip of the shadow.
Plugging in the values we know:
h / 1.41 = tan(55.3)
To find the value of tan(55.3), we can use a scientific calculator or an online calculator:
tan(55.3) ≈ 1.4281
Now we can solve for "h":
h / 1.41 = 1.4281
Multiplying both sides by 1.41:
h = 1.4281 * 1.41
h ≈ 2.0141
Therefore, the person's height is approximately 2.0141 meters.
To find the height of the person, we can use the concept of similar triangles.
Let's denote the height of the person as 'h' and the length of the shadow as 's'. We can consider two right triangles: one formed by the person, the person's shadow, and the Sun, and another formed by the person, their shadow, and the ground.
The angle between the person and the ground, which is the same angle between the ground and the Sun, is 34.7 degrees. This means the two triangles are similar, as they share an angle.
Knowing that the ratio of corresponding sides in similar triangles is equal, we can set up the following proportion:
h/s = tan(angle)
Given that the length of the shadow is 1.41 m and the angle is 34.7 degrees, we can substitute these values into the equation:
h/1.41 = tan(34.7)
To find the height, we can rearrange the equation to solve for 'h':
h = 1.41 * tan(34.7)
Now, we can calculate the height by substituting the values and evaluating the expression:
h = 1.41 * tan(34.7)
h ≈ 1.41 * 0.702
h ≈ 0.993 m
Therefore, the height of the person is approximately 0.993 meters.