Find the angle of elevation of the sun when a tree that is 10 yd tall cast a shadow 14 yds long

To find the angle of elevation of the sun, you can use the concept of similar triangles.

Let's denote the height of the tree as "h" and the length of the shadow as "s." In this case, h = 10 yards and s = 14 yards.

We can set up a proportion between the height of the tree, the length of the shadow, and the distance from the tree to the tip of the shadow, which will be equal to the tangent of the angle of elevation:

tan(angle) = h / s

Plugging in the values, we get:

tan(angle) = 10 / 14

To find the angle, we can take the inverse tangent (arctan) of both sides:

angle = arctan(10 / 14)

Using a calculator, you can find the approximate value of the angle of elevation. It is approximately 35.54 degrees.

Therefore, the angle of elevation of the sun when the tree casts a 14-yard long shadow is approximately 35.54 degrees.

To find the angle of elevation of the sun, we can use the tangent function. The angle of elevation is represented by the angle between the ground and the line from the top of the tree to the sun.

First, we need to determine the height of the tree's shadow. Since the shadow of the tree is 14 yds long and the tree itself is 10 yd tall, we can calculate the height of the shadow by multiplying the height of the tree by the ratio of the shadow length to the distance from the tree to the point where the shadow is measured.

Let's assume the distance from the tree to the point where the shadow is measured is "d". Therefore, we have:

Height of the shadow = Height of the tree × (Shadow length / Distance from tree to point of measurement)

Height of the shadow = 10 yd × (14 yd / d)

Now, we can use this information to find the angle of elevation. The tangent of the angle of elevation is given by:

Tangent(angle) = Height of the shadow / Distance from the tree to the point of measurement

Tangent(angle) = (10 yd × (14 yd / d)) / d

Now, we can solve this equation for the angle. Rearranging the equation, we have:

angle = arctan((10 yd × (14 yd / d)) / d)

To find the value of the angle, we need to know the value of "d" - the distance from the tree to the point where the shadow is measured. Once we have that information, we can substitute the value of "d" into the equation and calculate the angle using a calculator or trigonometric table.

Note: Make sure to convert the angle measurement to the desired units (e.g., degrees or radians) if necessary.

tanA = Y/X = 10/14. Solve for A.

35.5