All categories

2 years ago

Determine the value of each variable in the figure below. Keep answers in simplest radical form.

Mathematics

1 answer:

Tanzania [10]2 years ago

7 0

Answer:

a = 21

b = 63

c = 42√3

d = 21√3

Step-by-step explanation:

The sides of a 30°-60°-90° triangle have the ratios 1 : √3 : 2. The given side (42) is the longest side of the smallest triangle, and the shortest side of the largest triangle.

That means the other sides of the smallest triangle will be ...

a = 42/2 = 21

a+b = 2(42) = 84

b = (a+b) -a = 84 -21 = 63

d = 21√3 . . . . middle-length side of the smallest triangle

c = 42√3 . . . . middle-length side of the largest triangle

The values of the variables are ...

a = 21
b = 63
c = 42√3
d = 21√3

You might be interested in

What are the coordinates of vertex J of the pre-image?

bixtya [17]

The answer is:
(x , y)
(0,-4)

5 0

3 years ago

Given: AC bisects angle BCD , Angle ABC is congruent to angle ADC prove AB is congruent to AD. Help immediately

weeeeeb [17]

AC bisects ∠BAD, => ∠BAC=∠CAD ..... (1)

thus in ΔABC and ΔADC, ∠ABC=∠ADC (given),

∠BAC=∠CAD [from (1)],

AC (opposite side side of ∠ABC) = AC (opposite side side of ∠ADC), the common side between ΔABC and ΔADC

Hence, by AAS axiom, ΔABC ≅ ΔADC,

Therefore, BC (opposite side side of ∠BAC) = DC (opposite side side of ∠CAD), since (1)

Hence, BC=DC proved.

7 0

3 years ago

Read 2 more answers

Which equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4)? Check al

natka813 [3]

Find the slope of the line first:
5x - 2y = -6,
y = (5/2)x + 3;
Since we need a line that's perpendicular, m = - (2/5).

The only equation that has the slope of this m is 2x + 5y = -10;

8 0

3 years ago

Read 2 more answers

Find an exact value cos(19pi/12)

dmitriy555 [2]

$cos\left ( \frac{9\pi}{12}\right )=\frac{\sqrt{2-\sqrt{3}}}{2}$

Step-by-step explanation:

We know that

cos 2x = 2cos²x - 1

So we have

$cosx=\sqrt{\frac{1+cos2x}{2}}$

Substituting $x=\frac{19\pi}{12}$

$cos\left ( \frac{19\pi}{12}\right )=\sqrt{\frac{1+cos2\left ( \frac{19\pi}{12}\right )}{2}}\\\\cos\left ( \frac{19\pi}{12}\right )=\sqrt{\frac{1+cos\left ( \frac{19\pi}{6}\right )}{2}}\\\\cos\left ( \frac{9\pi}{12}\right )=\sqrt{\frac{1+cos570}{2}}\\\\cos\left ( \frac{9\pi}{12}\right )=\sqrt{\frac{1-\frac{\sqrt{3}}{2}}{2}}\\\\cos\left ( \frac{9\pi}{12}\right )=\sqrt{\frac{2-\sqrt{3}}{4}}\\\\cos\left ( \frac{9\pi}{12}\right )=\frac{\sqrt{2-\sqrt{3}}}{2}$

$cos\left ( \frac{9\pi}{12}\right )=\frac{\sqrt{2-\sqrt{3}}}{2}$

3 0

3 years ago

Read 2 more answers

What number is 25% of 400 please show work thank you

ANEK [815]

Answer:

100

Step-by-step explanation:

well, you can just use a calculator, or your mind if that's possible, to solve this.

at least, what i think you're asking.

400 × 0.25 = 100.

this one is extra easy because you should know that 25% is a quarter, and 400 can just be divided by 4 to get your answer.

6 0

2 years ago