From the top of a 52 m tall lighthouse, a sailboat is sighted at an angle of depression of 47°

The measure of an angle is 23 less than 5 times it’s supplement. Find the angle measurement. Show/explain work

sertanlavr [38]

Let the measure of an angle be "a"
let the supplement be "s"

a= s-23

8 0

3 years ago

What is the area of this figure?

lesantik [10]

Answer:

$\Huge\boxed {A =859ft^{2} }$

Step-by-step explanation:

Hello There!

To solve for the area of this figure we need to split the figure into 3 different parts:

A rectangle with a length of 9 ft and a width of 7 ft

a rectangle with a width of 9ft + 7ft and a length of 25 ft

a rectangle with a width of 18 ft and a length of 22 ft

To find the area of a rectangle we use the formula

$A=w*l$ where w = width and l = length

for the first one we plug in the values

A = 9 * 7

9 * 7 = 63 so the area of the smallest rectangle is 63ft²

Now lets find the area of the larger rectangle

The dimensions are l = 25 ft and w = 9 + 7 (16 ft)

Now we can plug in the values into the area formula

A = 16 * 25

16*25=400 so the area of the larger rectangle is 400 ft²

Now lets find the area of the last rectangle

The dimensions are l = 22 ft and w = 18 ft

now lets plug in the values to the formula

A = 22 * 18 =396

so the area of the last rectangle is 396 ft²

Finally we want to add all of the areas together

396 + 400 + 63 = 859

So the area of the figure is 859 ft²

7 0

3 years ago

Read 2 more answers

If the smallest angle of a triangle is 20° and it is included between sides of 4 and 7, then (to the nearest tenth) the smallest

lawyer [7]

Answer:

$3.5$

Step-by-step explanation:

The smallest side of a triangle is formed by the smallest angle in the triangle.

To find the side opposite (formed by) the 20 degree angle, we can use the Law of Cosines. The Law of Cosines states that for any triangle, $c^2=a^2+b^2-ab\cos \gamma$ , where $a$ , $b$ , and $c$ are the three sides of the triangle and $\gamma$ is the angle opposite to $c$ .

Let $c$ be the side opposite to the 20 degree angle.

Assign variables:

$a\implies 4$
$b\implies 7$
$\gamma \implies 20^{\circ}$

Substituting these variables, we get:

$c^2=4^2+7^2-2(4)(7)\cos 20^{\circ},\\c^2=16+49-56\cos 20^{\circ},\\c^2=12.377213236,\\c=\sqrt{12.377213236}=3.51812638147\approx \boxed{3.5}$

Therefore, the shortest side of this triangle is 3.5.

5 0

3 years ago

Someone please help or i’ll be failing geometry this year

Vlad [161]

Step-by-step explanation:

I don't know what constructions you were taught.

a "similar" triangle is a triangle with exactly the same angles as the other triangle, but the lengths of all sides are stretched or shortened by the same scaling factor f.

by saying 1:2 she means the second triangle should have sides with twice the lengths of the first triangle (f=2).

and the extra challenge - same basic thing. she allows you to pick one of the two triangles as reference. and then you need to draw a third triangle (again with the same angles) with the side lengths extended by the scaling factor f of 4/3.

I would draw the triangles right on top of each other with the same starting corner (let's call it A) for all 3.

we would get the triangles ABC, AMN and AXY.

the points B and C would be then halfway on AM and AN.

and M and N would then a bit before X and Y on AX and AY.

the beauty is, you only need to construct 2 sides of every new triangle down to the new endpoints. the third side is automatically scaled correctly, and you only need to connect these new endpoints.

let's assume you draw a triangle (just very simple) ABC with all side lengths being 3. so, AB=3, AC=3, BC=3.

now you draw AMN by extending AB and AC to a side length of 6 (f=2) creating M and N, and you connect M and N.

and then you can create the third triangle AXY by extending AM and AN by a factor of 4/3 to side lengths of 8 (4/3 × 6 = 8) creating new end points X and Y. and you connect X and Y.

and that is it. all 3 triangles are similar (the same angles), and all sides of a triangle have the same length ratio to the sides of the other triangle(s).

4 0

3 years ago

Need help fast!!!!!!!!

Kamila [148]

C. 2/3; reduction
have a good day

4 0

3 years ago