Answer: 0.55
Step-by-step explanation:
According to the trigonometry, in a right triangle :
[tex]\sin\theta=\dfrac{\text{Side opposite to }\theta}{\text{Hypotenuse}}[/tex]
Given : A 50-foot tree casts a shadow 75 feet long.
Here , Side opposite to [tex]\theta[/tex] = 50 feet
In right triangle formed by tree , Let the hypotenuse be h.
According to the Pythagoras theorem, we have
[tex]h^2=(50)^2+(75)^2\\\\ h^2=2500+5625=8125\\\\ h=\sqrt{8125}=90.1387818866\approx90.14[/tex]
Then,
[tex]\sin\theta=\dfrac{50}{90.14}=0.554692700244\approx0.55[/tex]
Hence, the sine of the angle between the ground and the line that connects the tip of the shadow to the top of the tree is approximately 0.55.
