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3 years ago

Finding the tangent of angle E

Mathematics

2 answers:

Pavlova-9 [17]3 years ago

3 0

I don’t know but I need an answer

lozanna [386]3 years ago

3 0

Answer:

tan(E) = $\sqrt{3\\}$

Step-by-step explanation:

Given: ED = 4 $\sqrt{6}$ and CD = 6 $\sqrt{2\\}$

Step 1 : Find CE

ED² = CE² + CD²

(4√6)² = (CE)² + (6√2)²

96 = CE² + 72

24 = CE²

CE = 2√6

Step 2 : Find ∠E using side lengths

Based on our leg lengths : 6√2 & 2√6 , we can conclude that this is a

30-60-90 triangle (the sqaures are opposites yk)

Because 6√2 is the larger leg, and ∠E is opp side of CD,

∠E = 60

From there all you do is find the tangent with a calculator "tan(60)"

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Alex73 [517]

Answer:

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Step-by-step explanation:

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3 years ago

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Find the surface area of the following figure.

fgiga [73]

Answer:

$\boxed{\textsf{\pink{ Hence the TSA of the cuboid is $\sf 32x^2$}}}.$

Step-by-step explanation:

A 3D figure is given to us and we need to find the Total Surface area of the 3D figure . So ,

From the cuboid we can see that there are 5 squares in one row on the front face . And there are two rows. So the number of squares on the front face will be 5*2 = 10 .

We know the area of square as ,

$\qquad\boxed{\sf Area_{(square)}= side^2}$

Hence the area of 10 squares will be 10x² , where x is the side length of each square. Similarly there are 10 squares at the back . Hence their area will be 10x² .

Also there are in total 12 squares sideways 6 on each sides . So their surface area will be 12x² . Hence the total surface area in terms of side of square will be ,

$\sf\implies TSA_{(cuboid)}= 10x^2+10x^2+12x^2\\\\\sf\implies\boxed{\sf TSA_{(cuboid)}= 32x^2}$

Now let's find out the TSA in terms of side . So here the lenght of the cuboid is equal to the sum of one of the sides of 5 squares .

$\sf\implies 5x = l \\\\\sf\implies x = \dfrac{l}{5} \\\\\qquad\qquad\underline\red{ \sf Similarly \ breadth }\\\\\sf\implies b = 3x \\\\\sf\implies x = \dfrac{ b}{3}$

$\rule{200}2$

Hence the TSA of cuboid in terms of lenght and breadth is :-

$\sf\implies TSA_{(cuboid)}= 10x^2+10x^2+12x^2\\\\\sf\implies TSA_{(cuboid)}= 20\bigg(\dfrac{l}{5}\bigg)^2+12\bigg(\dfrac{b}{3}\bigg) \\\\\sf\implies TSA_{(cuboid)}= 20\times\dfrac{l^2}{25}+12\times \dfrac{b^2}{9}\\\\\sf\implies \boxed{\red{\sf TSA_{(cuboid)}= \dfrac{4}{5}l^2 +\dfrac{4}{3}b^2 }}$