All categories

3 years ago

In ΔDEF, e = 2.7 inches, ∠F=49° and ∠D=58°. Find the length of f, to the nearest 10th of an inch.

Mathematics

1 answer:

Anton [14]3 years ago

7 0

Answer:2.1

Step-by-step explanation:

\text{Draw a diagram:}

Draw a diagram:

e = 2.7

f = ?

49°

58°

\text{A.S.A.}\rightarrow \text{Law of Sines}

A.S.A.→Law of Sines

\frac{a}{\sin A}=\frac{b}{\sin B}

sinA

sinB

\text{Find other angle:}

Find other angle:

\angle E=180-49-58=73^{\circ}

∠E=180−49−58=73

∘

e = 2.7

f = ?

49°

58°

73°

\frac{f}{\sin 49}=\frac{2.7}{\sin 73}

sin49

sin73

2.7

f=\frac{2.7\sin 49}{\sin 73} \approx 2.131 \approx 2.1

sin73

2.7sin49

≈2.131≈2.1

You might be interested in

Which set of shapes contains members that are always similar to one another?

Elden [556K]

It should be C. Equilateral triangles

4 0

3 years ago

Read 2 more answers

A bookstore bought a case of 10 books at a wholesale price of $84. The bookstore will sell the books at a 25 percent markup, and

Gekata [30.6K]

Answer:

I am pretty sure that it is 105 dollars

5 0

3 years ago

Read 2 more answers

Write an algebraic expression for each verbal expression. Then simplify, indicating the properties used. 4 times the difference

MissTica

4(f ^2-g)+f^2+2g is your answer

6 0

3 years ago

If the first step in the solution of the equation 2x - 8 = 5x + 3 is "subtract 2x," then in the form of a paragraph, explain in

monitta

$x = \frac{-11}{3}$

<u>Step-by-step explanation:</u>

Here we have , If the first step in the solution of the equation 2x - 8 = 5x + 3 is "subtract 2x," then in the form of a paragraph, explain in complete sentences the next steps necessary to completely solve the equation for x. Let's solve this :

2x - 8 = 5x + 3

⇒ $2x - 8 = 5x + 3$

⇒ $(2x - 8)-2x = (5x + 3)-2x$ { subtract 2x from both side }

⇒ $0 - 8 = 5x-2x + 3$

⇒ $- 8 = 3x + 3$

⇒ $- 8 -3= 3x + 3-3$ { subtract 3 from both sides }

⇒ $- 11 = 3x + 0$

⇒ $- 11 = 3x$

⇒ $\frac{-11}{3} = \frac{3}{3} x$ { divide 3 from both sides }

⇒ $x = \frac{-11}{3}$

3 0

3 years ago

Martin throws a ball straight up in the air. the equation h(t) = -16t^2 + 40t + 5 gives the height of the ball, in feet, t secon

Lisa [10]

Answer:

2.62 seconds

Step-by-step explanation:

Let

t ----> the time in seconds

h(t) ----> he height of the ball, in feet

we have

$h(t)=-16t^2+40t+5$

we know that

When the ball hits the ground, the height is equal to zero

$-16t^2+40t+5=0$

The formula to solve a quadratic equation of the form

$at^{2} +bt+c=0$

is equal to

$t=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$-16t^2+40t+5=0$

$a=-16\\b=40\\c=5$

substitute in the formula

$t=\frac{-40\pm\sqrt{40^{2}-4(-16)(5)}} {2(-16)}$

$t=\frac{-40\pm\sqrt{1,920}} {-32}$

$t=\frac{-40+\sqrt{1,920}} {-32}=-0.12\ sec$

$t=\frac{-40-\sqrt{1,920}} {-32}=2.62\ sec$

therefore

The solution is t=2.62 seconds

4 0

3 years ago