^ LOL for real. but whatever they said
Answer:
Volume = 480 cubic inches
Explanation:
We have the following relationships to work with
width w = h -3
length l = h + 4
area of base of prism a = l x w = 60 (1)
area of base in terms of h = (h-3)(h+4) =h² -3h + 4h -12 (2)
Setting (1) = (2) gives
h² + h -12 =60
h² + h -72 = 0
Factoring the LHS we get
(h+9)(h-8) = 0
The solutions for h are
h + 9 = 0 ==> h = -9
h - 8 = 0 ==> h = 8
Since h cannot be negative, h = 8 inches
Volume = base area x h = 60 x 8 = 480 cubic inches
<u>Note</u>
We do not have to calculate length and width separately, but if so,
w = 8 -3 = 5
l = 8 + 4 = 12
The angle of the triangle ABC from smallest to largest are approximately 22°, 27° and 131°.
The sides of the triangle are as follows;
AB = 20
BC = 12
AC = 10
Let's find ∠A using cosine rule,
a² = b² + c² - 2bc cos A
cos A = b² + c² - a² / 2bc
Therefore,
cos A = 10² + 20² - 12² / 2 × 10 × 20
cos A = 100 + 400 - 144 / 400
cos A = 356 / 400
cos A = 0.89
A = cos⁻¹ 0.89
A = 27.1267531173
∠A ≈ 27°
Using sine rule let's find ∠B
12 / sin 27 = 10 / sin B
cross multiply
12 sin B = 10 sin 27
sin B = 10 sin 27 / 12
sin B = 10 × 0.45399049974 / 12
sin B = 4.5399049974 / 12
B = sin⁻¹ 0.37832541645
B = 22.2299936087
∠B = 22°
Using sum of triangle theorem let's find ∠C
∠C = 180 - 27 - 22
∠C = 131°
The angles from smallest to largest are approximately 22°, 27° and 131°.
learn more on triangle here: brainly.com/question/12913110?referrer=searchResults
THE ANSWER IS A HURRY UPPPP
