Answer:
Below in bold.
Step-by-step explanation:
sin 66.4 = opposite side / hypotenuse
sin 66.4 = 21.3 / y
y = 21.3 / sin 66.4
y = 23.24.
tan 66.4 = 21.3 / x
x = 21.3 / tan 66.4
x = 9.31.
Answer: a) The figure can be reasonably divided into two geometries:
• a rectangular prism
• a hemisphere.
b) The volume of the rectangular prism is given by
V = lwh
V = (10 cm)(5 cm)(4 cm) = 200 cm³
The volume of the hemisphere is given by
V = (2π/3)r³
V = (2π/3)(3 cm)³ = 18π cm³
c) The total volume of the figure is
total volume = (prism volume) + (hemisphere volume)
V = 200 cm³ + 18π cm³
V ≈ 256.549 cm³
Step-by-step explanation:
The altitude to the hypotenuse of a right triangle is the mean proportional between the segments into which it divides the hypotenuse ⇒<span>
</span>altitude = √(9*3) = √27
<span>By the Pythagorean theorem:
y = </span>√(9² + (√27)²) = √(81+27) = √108 = 6√3 ← answer
