Answer:
The building is 187.5 feet tall.
Step-by-step explanation:
A nearby person is 6 feet tall, and casts a shadow that is 8 feet long.
This means that the relation between the real height and the shadow is given by:
A tall building casts a shadow that is 250 feet long. How tall is the building?*
The real height is three fourths of the shadow. So
The building is 187.5 feet tall.
Cgagcadhfhfjooguo! duolujto
Set up a proportion:
6 feet over 11 feet long equals x feet over 33 feet long
6/11 = x/33
198 = 11x
x = 18
The height of the tree is 18 feet tall
Step-by-step explanation:
Left hand side:
4 [sin⁶ θ + cos⁶ θ]
Rearrange:
4 [(sin² θ)³ + (cos² θ)³]
Factor the sum of cubes:
4 [(sin² θ + cos² θ) (sin⁴ θ − sin² θ cos² θ + cos⁴ θ)]
Pythagorean identity:
4 [sin⁴ θ − sin² θ cos² θ + cos⁴ θ]
Complete the square:
4 [sin⁴ θ + 2 sin² θ cos² θ + cos⁴ θ − 3 sin² θ cos² θ]
4 [(sin² θ + cos² θ)² − 3 sin² θ cos² θ]
Pythagorean identity:
4 [1 − 3 sin² θ cos² θ]
Rearrange:
4 − 12 sin² θ cos² θ
4 − 3 (2 sin θ cos θ)²
Double angle formula:
4 − 3 (sin (2θ))²
4 − 3 sin² (2θ)
Finally, apply Pythagorean identity and simplify:
4 − 3 (1 − cos² (2θ))
4 − 3 + 3 cos² (2θ)
1 + 3 cos² (2θ)
