The volume of this triangular prism is 120 cubic meters. What is the value of y? Please help!!

Mathematics

1 answer:

MakcuM [25]3 years ago

3 0

<h3>Answer: y = 6</h3>

The triangle has a base of y and a height of 5. The area of the triangle is

area = (1/2)*base*height = 0.5*y*5 = 2.5y

which multiplies with the prism's depth 8 to get 2.5y*8 = 20y

The expression 20y represents the volume of the prism, which we are told is 120 cubic meters, so 20y = 120 solves to y = 6 after dividing both sides by 20.

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a. This is a right triangle with two sides and one angle given.

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$\frac{a}{Sin \ A}=\frac{b}{Sin \ B}=\frac{b}{Sin \ C}$

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$\frac{17}{Sin \ 90 \textdegree}=\frac{10}{Sin \ m\angle B}\\\\m\angle B=Sin^{-1}\frac{10}{(17/Sin \ 90\textdegree)}\\\\=36.03\textdegree$

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$\frac{a}{Sin \ a}=\frac{b}{Sin \ B}\\\\\frac{15}{Sin \ 90\textdegree}=\frac{9}{Sin \ w\textdegree}\\\\\\\\w=Sin^{-1}(\frac{9}{15}), \ \ Sin \ 90\textdegree=1\\\\=36.87\textdegree$