Answer: 7 7/8 hours long
Step-by-step explanation:
April worked 1 1/2 times as long as Carl did. 1 1/2 can be rewritten as 3/2. Number of Hours April worked on math project 3/2 times the Number of Hours Carl worked on Math project. Which Carl worked 5 1/4 hours long, which can be rewritten as 21/4
Of course A does because integers are positive and negative
<u>Given</u>:
The base of each triangular base is 42 m.
The height of each triangular base is 20 m.
The sides of the triangle are 29 m each.
The height of the triangular prism is 16 m.
We need to determine the surface area of the triangular prism.
<u>Surface area of the triangular prism:</u>
The surface area of the triangular prism can be determined using the formula,
where b is the base of the triangle,
h is the height of the triangle,
s₁, s₂ and s₃ are sides of the triangle and
H is the height of the prism.
Substituting the values, we get;
Thus, the surface area of the triangular prism is 2440 m²
Answer:
12.1 cm
Step-by-step explanation:
Using the law of sines, we can find angle C. Then from the sum of angles, we can find angle B. The law of sines again will tell us the length AC.
sin(C)/c = sin(A)/a
C = arcsin((c/a)sin(A)) = arcsin(8.2/13.5·sin(81°)) ≈ 36.86°
Then angle B is ...
B = 180° -A -C = 180° -81° -36.86° = 62.14°
and side b is ...
b/sin(B) = a/sin(A)
b = a·sin(B)/sin(A) = 13.5·sin(62.14°)/sin(81°) ≈ 12.0835
The length of AC is about 12.1 cm.
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<em>Comment on the solution</em>
The problem can also be solved using the law of cosines. The equation is ...
13.5² = 8.2² +b² -2·8.2·b·cos(81°)
This is a quadratic in b. Its solution can be found using the quadratic formula or by completing the square.
b = 8.2·cos(81°) +√(13.5² -8.2² +(8.2·cos(81°))²)
b = 8.2·cos(81°) +√(13.5² -(8.2·sin(81°))²) . . . . . simplified a bit
