Consider the two triangles shown below are the two triangles congruent

Mathematics

1 answer:

mixer [17]2 years ago

7 0

Answer: Yes

Step-by-step explanation: Let's first find the missing angle in the second triangle and to find this angle, remember that the sum of the measures of a triangle is 180 degrees so you should find that our missing angle is 67°.

Now, notice that we have two angles and the included side of one triangle

congruent to two angles and the included side of a second triangle.

Therefore, we can say the triangles are congruent by ASA.

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Dolve for theta. С 13 4 o o A B Your answer

ANTONII [103]

Answer:

θ ≈ 17.1°

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan θ = $\frac{opposite}{adjacent}$ = $\frac{BC}{AC}$ = $\frac{4}{13}$ , then

θ = $tan^{-1}$ ( $\frac{4}{13}$ ) ≈ 17.1° ( to the nearest tenth )

5 0

3 years ago

A rectangular solid with a square base has a volume of 4096 cubic inches - determine the dimensions that yield the minimum surfa

Bumek [7]

Answer:

side of base, a = 10.1 inches, height, h = 40.1 inches

Step-by-step explanation:

Volume of rectangular solid, V = 4096 cubic inches

Let the side of base is a and the height is h.

$V = a^2h\\\\4096 = a^2 h ..... (1)$

surface area of the solid

$S = 2a^2 + 4 ah \\\\S = 2a^2 + 4 \times a \times \frac{4096}{a^2} from (1)\\\S = 2a^2 + \frac{4096}{a}\\\\\frac{dS}{da}= 4 a - \frac{4096}{a^2}\\\\4 a - \frac{4096}{a^2} = 0 \\\\a^3 = 1024\\\\a =10.1 inches$