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Bezzdna [24]
4 years ago
8

The height of a trapezoid is 8 inches and it’s area is 96 inches. One base of the trapezoids is 6 inches longer than the other b

ase. What are the lengths of the bases? Explain how you found your answer
Mathematics
1 answer:
KonstantinChe [14]4 years ago
7 0
There is a common equation we use to find the Area of a trapezoid.
(a+b)h/2=A
Let's fill in what we know. We're not going to fill in any information about the bases.
(a+b)8/2=96
We can already tell that 8/2 will simplify to 4.
(a+b)4=96
Let's divide each side by 4.
a+b=24
Now, let's look at the information about the bases.
So, we will have this in terms of base a, since one base is longer than the other. This is how it'll look.
a +(a+6)=24
We can simplify that further.
2a+6=24
now subtract 6 from each side.
2a=18
Let's divide
9=a
So one side is 9, so the other one is 15. We should make sure everything makes sense by putting all the information in the formula to find area.
(9+15)8/2
24×4
96.
The lengths of the bases are 9 and 15 inches.

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Answer:

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Step-by-step explanation:

Given the statement: An observer on top of a 50-foot tall lighthouse sees a boat at a 7° angle of depression.

Let x foot be the distance of the object(boat) from the base of the lighthouse

Angle of depression = 7^{\circ}

\angle CAB = \angle DCA = 7^{\circ}       [Alternate angle]

In triangle CAB:

To find AB = x foot.

Using tangent ratio:

\tan (\theta) = \frac{Opposite side}{Adjacent Base}

\tan (\angle CAB) = \frac{BC}{AB}

Here, BC = 50 foot and \angle CAB =7^{\circ}

then;

\tan (7^{\circ}) = \frac{50}{x}

or

x = \frac{50}{\tan 7^{\circ}}

x = \frac{50}{0.1227845609}

Simplify:

AB = x = 407.217321 foot

Therefore, the boat from the base of the light house is, 407.22'





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Tpy6a [65]

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A F is 13 using pythagorean theorem on triangle CED and applying the hypotenuse length to A F.

ABC is similar to triangle CED and is dilated by a factor of 3  so the base is 36.

using pythagorean theorem on triangle ABC gets the hypotenuse length of 39 which can be applied to FE

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