Answer:
M = 4.33885225095
Step-by-step explanation:
Area of the square ABFE = 10² = 100
M = 100 - (2P + Q)
Let’s calculate 2P + Q :
The area 2P + Q = area ΔABC + area of sector ACE + area of sector BCF
Note :
ΔABC is an equilateral triangle
m∠CBF = m∠CAE = 30°
area ΔABC = (CG × AB)÷2 = (8.660254037844×10)÷2 = 43.30127018922
CG = √(10^2 - 5^2)=8.660254037844 (Pythagorean theorem)
area of sector BCF = area ΔACE = 100π ÷ 12 = (8.333333333333)π
then
Area 2P + Q = area ΔABC + area sector ACE + area sector BCF
= 43.30127018922+(100÷12)π+(100÷12)π
= 43.30127018922+ (8.333333333333)π + (8.333333333333)π
= 95.66114774905
Conclusion:
M = 100 - (2P + Q) = 100-95.66114774905 = 4.33885225095
Answer:
20.833 feet
Step-by-step explanation:
The light reflects off the mirror at the same angle that it hits it at. So the triangle formed by the beam and mirror is similar to the triangle formed by Kevin and the mirror.
Therefore, we can write and solve a proportion.
h / 10 = 6.25 / 3
h = 20.833
The beam is 20.833 feet tall.
