9514 1404 393
Answer:
A. 201 cm³
Step-by-step explanation:
To find the volume, we need to know the length of the prism and the area of the triangular base.
We can find the area of the triangular base a couple of ways. Since we are given some angles, the convenient way will be to make use of those angles.
The triangular base is isosceles. For our purpose, we assume that means AB = BC. If we define point M as the midpoint of AC, then triangle BMC is a right triangle with a base of (9 cm/2) = 4.5 cm.
The side BC can be found from the trig relation ...
cos(∠BCA) = CM/BC
BC = CM/cos(∠BCA) = (4.5 cm)/cos(50°) ≈ 7.00
Then the area of the end triangle ABC is ...
base area = (1/2)(AC)(BC)sin(50°)
base area = (1/2)(9 cm)(7 cm)sin(50°) ≈ 24.133 cm²
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The length CF can be found from the relation ...
tan(40°) = EF/CF
CF = EF/tan(40°) = (7.00 cm)/tan(40°) ≈ 8.343 cm
Then the volume of the prism is ...
V = Bh
V = (24.133 cm²)(8.343 cm) ≈ 201 cm³
The volume of this isosceles triangular prism is about 201 cm³.
