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?
1 answer:
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 °
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The part of interest is the law of sines tells you
.. A = arcsin((12/11)*sin(46°)) = 51.7° . . . or . . . 180°-51.7° = 128.3°
.. c = 11*sin(82.3°)/sin(46°) ≈ 15.2 . . . or . . . sin(5.7°)/sin(46°) ≈ 1.5
Selection D is appropriate.
The part of interest is the law of sines tells you
.. A = arcsin((12/11)*sin(46°)) = 51.7° . . . or . . . 180°-51.7° = 128.3°
.. c = 11*sin(82.3°)/sin(46°) ≈ 15.2 . . . or . . . sin(5.7°)/sin(46°) ≈ 1.5
Selection D is appropriate.