Write an equation to represent the following statement. j is 7times as large as 6 .

In ΔBCD, the measure of ∠D=90°, the measure of ∠C=77°, and CD = 41 feet. Find the length of BC to the nearest foot.

OLga [1]

Answer:

182 ft

Step-by-step explanation:

When you are not given a diagram, always draw one for yourself (see diagram).

When you have a right triangle (triangle with 90° angle), you can use the trigonometry ratios, You can remember them using SohCahToa. It is read like this:

sinθ = opposite/hypotenuse Soh

cosθ = adjacent/hypotenuse Cah

tanθ = opposite/adjacent Toa

"θ" means the angle of reference (the angle you are talking about).

We are looking for the length of BC, which is the hypotenuse. I labelled it "d" (lowercase D) because it is opposite to ∠D.

We know ∠C = 77°. This will be our angle of reference (replace θ).

The side we know is DC, also known as "b" (lowercase B) because it's opposite to ∠B. "b" is the adjacent side when θ = C because "b" is touching ∠C.

Take the general trig. formula that has hypotenuse and adjacent: (cosine ratio)

cosθ = adjacent/hypotenuse

Substitute the variables specific for this problem.

cosC = b/d

Substitute the values you know.

cos77° = (41 ft) / d

Isolate "d" to the left side

dcos77° = $d*\frac{41ft}{d}$ Multiply both sides by "d"

dcos77° = 41 ft

dcos77° / cos77° = 41 ft / cos77° Divide both sides by cos77°

d = 41 ft / cos77° Input into calculator

d = 182.261874....... ft Unrounded answer

d ≈ 182 ft Rounded to nearest foot (whole number)

Remember d = BC. It's often easier to use one letter for calculations.

Therefore the length of BC is about 182 feet.

8 0

3 years ago

Kenneth displays his picture frames

stellarik [79]

What that's not a question lol

3 0

3 years ago

PLZ HURRY IT'S URGENT!!!!!!

Anton [14]

I think the correct answer your looking for is D) 9

5 0

3 years ago

Read 2 more answers

×+4×+2=7+5+2× Can u solve that please?????

KiRa [710]

Hey! if this is algebra i recommend getting this app called "Math PAPA" it really helped me out when i was in algebra

7 0

3 years ago

Read 2 more answers

What is the area of a sector with a central angle of 8 π/11 radians and a radius of 7.2 ft? use 3.14 for π and round your final

coldgirl [10]

Answer:

$59.19 ft^2$

Step-by-step explanation:

step 1

Find the area of the circle

The area of the circle is equal to

$A=\pi r^{2}$

we have

$r=7.2\ ft$

$\pi =3.14$

substitute

$A=(3.14)(7.2)^{2}$

$A=162.78\ ft^2$

step 2

we know that

The area of a circle subtends a central angle of 2π radians

so

using proportion

Find out the area of a sector with a central angle of 8 π/11 radians

$\frac{162.78}{2\pi }\frac{ft^2}{rad} =\frac{x}{(8\pi/11)}\frac{ft^2}{rad} \\\\x=162.78(8/11)/2\\\\x=59.19\ ft^2$

7 0

3 years ago