Question

A 96 ft tree casts a shadow that is 120 ft long. What is the angle to the nearest hundredth the sun makes with the ground?

Answer 1

Answer:

The angle to the nearest hundredths is 38. 66 °

Step-by-step explanation:

From the question above the events will form a right angle triangle.  From the triangle above the opposite side is the height of the tree. The adjacent side is the length of the shadow. The x value is the angle formed.

From the triangle,

height of tree (opposite) = 96 ft

length of shadow(adjacent) = 120 ft

angle formed = x

Using the SOHCAHTOA principle,

tan x = opposite/adjacent

tan x = 96/120

tan x = 0.8

x = arctan(0.8)

x =  38.659808254

6, immediately after the decimal → tenth value

5  → hundredth value

9  → thousandth value

The thousandth value(9) is greater than 5 so we give 1 to the hundredth value(5) to make it 6.

To the nearest hundredth ,

x = 38. 66 °