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JulsSmile [24]
3 years ago
11

David made a class banner out of a large rectangular piece of paper. He cut a

Mathematics
1 answer:
Irina18 [472]3 years ago
6 0

Answer:

100 in²

Step-by-step explanation:

The area of the banner is equal to the area of the initial rectangle minus the area of the cutout triangle.

The rectangle has a height of 8 inches and width of 14 inches, so its area is:

A = (8 in) (14 in) = 112 in²

The triangle has a base of 8 inches and a height of 3 inches, so its area is:

A = ½ (8 in) (3 in) = 12 in²

So the area of the banner is 112 in² − 12 in² = 100 in².

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An observer on top of a 50-foot tall lighthouse sees a boat at a 7° angle of depression. To the nearest foot, how far is the boa
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Answer:

407.22 foot is the boat from the base of the lighthouse

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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