1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
never [62]
3 years ago
7

Triangle F G E is shown. Angle F E G is a right angle. The length of hypotenuse F G is 18.6 inches and the length of F E is 12 i

nches. Angle F G E is x. Which is the best approximation for the measure of angle EGF? 32.8° 40.2° 49.8° 57.2°

Mathematics
1 answer:
Delicious77 [7]3 years ago
8 0

Answer:

Measure of ∠FGE is 40.2°.

Step-by-step explanation:

Refer to the attachment.

Consider ΔFGE. Given that ∠FEG = 90° and ∠FGE is x°.

To find the value of ∠FGE use trigonometric ratios.

Use sine ratio to find the value of ∠FGE.

\sin \theta=\dfrac{opposite\:side}{hypotenuse\:side}

Rewriting it in terms of x° as follows,

\sin x=\dfrac{opposite\:side}{hypotenuse\:side}

Now find the opposite and hypotenuse side of the angle ∠FGE.

So opposite side of ∠FGE is FE and hypotenuse side of ∠FGE is FG.

Substituting the values,

\sin x=\dfrac{FE}{FG}

Given that length of FE is 12 inch and FG is 18.6 inch.

Substituting the value,

\sin x=\dfrac{12}{18.6}

To find the value of x, taking inverse sin.

x=\arcsin \left(\dfrac{12}{18.6}\right)

Calculating the value,

x=40.17

Rounding to nearest tenth the value of angle is 40.2

Therefore measure of ∠FGE is 40.2° .

You might be interested in
Using the formula in model 1, choose the correct answers for the new balance and the amount of interest earned in the following
poizon [28]
Total = Principal * (1 + rate)^years
Total = 650 * (1.08)^14
<span>Total = 1,909.1</span>8

5 0
3 years ago
What is the range of the function y=3(x+8? -0​
gladu [14]

Answer:

The answer is A, -∞ < y < ∞

8 0
3 years ago
Solve the equation for principal values of x. Express solutions in degrees.
Hitman42 [59]

Option C:

x = 90°

Solution:

Given equation:

\sin x=1+\cos ^{2} x

<u>To find the degree:</u>

\sin x=1+\cos ^{2} x

Subtract 1 + cos²x from both sides.

\sin x-1-\cos ^{2} x=0

Using the trigonometric identity:\cos ^{2}(x)=1-\sin ^{2}(x)

\sin x-1-\left(1-\sin ^{2}x\right)=0

\sin x-1-1+\sin ^{2}x=0

\sin x-2+\sin ^{2}x=0

\sin ^{2}x+\sin x-2=0

Let sin x = u

u^2+u-2=0

Factor the quadratic equation.

(u+2)(u-1)=0

u + 2 = 0,  u – 1 = 0

u = –2, u = 1

That is sin x = –2, sin x = 1

sin x can't be smaller than –1 for real solutions. So ignore sin x = –2.

sin x = 1

The value of sin is 1 for 90°.

x = 90°.

Option C is the correct answer.

3 0
2 years ago
Read 2 more answers
What is the volume of this pyramid? 945 cm³ 1260 cm³ 1890 cm³ 2520 cm³ A pyramid with a right triangular base. The right triangu
notsponge [240]

Answer:

The volume of the pyramid is 1,260\ cm^{3}

Step-by-step explanation:

we know that

The volume of the triangular pyramid is equal to

V=\frac{1}{3}BH

where

B is the area of the triangular base

H is the height of the pyramid

step 1

Find the area of the base B

B=\frac{1}{2}bh

we have

b=14\ cm

h=18\ cm

substitute

B=\frac{1}{2}(14)(18)=126\ cm^{2}

step 2

Find the volume

we have

B=126\ cm^{2}

H=30\ cm

substitute

V=\frac{1}{3}BH

V=\frac{1}{3}(126)(30)=1,260\ cm^{3}

5 0
3 years ago
Read 2 more answers
A snack tray at a party has cheese squares with 2 grams of protein apiece and turkey slices with 3 grams of protein apiece. Whic
Andreyy89

Answer:

The inequality equation is 12 ≤ 2x + 3y

Step-by-step explanation:

Protein in a cheese square = 2 grams

Protein in a turkey square = 3 grams

And She can eat 12 or more grams of proteins

Let x be the number of cheese squares and y be the number of turkey squares that she eats.

So, we can write an inequality equation, that describes the given situation in the problem.

i.e. 2x + 3y ≥ 12  or 12 ≤ 2x + 3y

So the inequality equation is 12 ≤ 2x + 3y

4 0
3 years ago
Read 2 more answers
Other questions:
  • On Monday, Brad biked 1 4/6 miles; Tuesday, 1 3/6 miles; Wednesday, 1 5/6 miles; and Thursday, 1 4/6 miles. On which day did he
    12·2 answers
  • Please help me with this i will mark you brainliest ​
    5·2 answers
  • In the expression 73 – 4•3+8, the first operation is...? A.an exponent
    9·1 answer
  • What are all the factors of 32?
    9·1 answer
  • 6) (4 x 2)5 + 6^2 - 4 = <br> plz help<br> i am in sixgrade
    14·1 answer
  • Help mw with thes two plz owo
    6·1 answer
  • Solve for x<br> 1+x&gt;2(-2-5x)+6x
    5·1 answer
  • Slope = 1; y-intercept = -4<br> in slope intercept form
    14·2 answers
  • When multiplying a vector by a positive scalar number, the vectors _____ stays the same
    15·1 answer
  • ASAP PLS I NEED IT AND TY
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!