Can anyone find the answer to this?

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

PLS HELP WILL GIVE BRAINLIEST :)

Rus_ich [418]

Step-by-step explanation:

the slope intercept form is

y = ax + b

"a" being the slope, "b" being the y- intercept (which is the y-value when x = 0).

the slope here :

in the table x is always increasing by 2.

and y is always investing by 1.

so, the slope is 1/2

the y-intercept :

we need to find the y-value for x = 0.

but we don't have a data point with x = 0 in the table.

so, we have to extend the structure of the table to the left.

x decreases by 2 (making it 0), and y decreases by 1 (making it -1).

therefore, the y- intercept (b) is -1.

and the line equation is

y = (1/2)x - 1

not sure about "the other method".

there is the point-slope form of the equation :

y - y1 = a(x - x1)

again with "a" begin the slope, and (x1, y1) being a point on the line.

if we get the y-intercept in the table, then this point is (0, y1).

and the equation would be

y - y1 = ax

in our case

y + 1 = (1/2)x

and another method ?

sometimes people write

nx + my = c

in our case starting with the original equation

y = (1/2)x - 1

2y = x - 2

-x + 2y = -2

x - 2y = 2

6 0

2 years ago

Help pls!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

postnew [5]

Answer?

What do you need help with? :)

5 0

2 years ago

What is the end behavior of f(x) = 5x 3 - 2x + 5?

Setler [38]

Answer:

It falls to the left and falls to the right. You can use Geogebra. There you just type the formula and it makes graph from which you can see the directions

6 0

3 years ago

Read 2 more answers

Write an inequality for this situation:You are driving, and the maximum speed limit is 55

aleksandr82 [10.1K]

Answer:

c

Step-by-step explanation:

5 0

2 years ago